diff --git a/pandas/_libs/window/indexers.pyx b/pandas/_libs/window/indexers.pyx
index 9af1159a805ec..ae67f5909eb56 100644
--- a/pandas/_libs/window/indexers.pyx
+++ b/pandas/_libs/window/indexers.pyx
@@ -11,7 +11,7 @@ def calculate_variable_window_bounds(
     int64_t num_values,
     int64_t window_size,
     object min_periods,  # unused but here to match get_window_bounds signature
-    object center,  # unused but here to match get_window_bounds signature
+    object center,
     object closed,
     const int64_t[:] index
 ):
@@ -30,7 +30,7 @@ def calculate_variable_window_bounds(
         ignored, exists for compatibility
 
     center : object
-        ignored, exists for compatibility
+        center the rolling window on the current observation
 
     closed : str
         string of side of the window that should be closed
@@ -45,6 +45,7 @@ def calculate_variable_window_bounds(
     cdef:
         bint left_closed = False
         bint right_closed = False
+        bint center_window = False
         int index_growth_sign = 1
         ndarray[int64_t, ndim=1] start, end
         int64_t start_bound, end_bound
@@ -62,6 +63,8 @@ def calculate_variable_window_bounds(
 
     if index[num_values - 1] < index[0]:
         index_growth_sign = -1
+    if center:
+        center_window = True
 
     start = np.empty(num_values, dtype='int64')
     start.fill(-1)
@@ -76,14 +79,27 @@ def calculate_variable_window_bounds(
     # right endpoint is open
     else:
         end[0] = 0
+    if center_window:
+        for j in range(0, num_values+1):
+            if (index[j] == index[0] + index_growth_sign*window_size/2 and
+               right_closed):
+                end[0] = j+1
+                break
+            elif index[j] >= index[0] + index_growth_sign * window_size/2:
+                end[0] = j
+                break
 
     with nogil:
 
         # start is start of slice interval (including)
         # end is end of slice interval (not including)
         for i in range(1, num_values):
-            end_bound = index[i]
-            start_bound = index[i] - index_growth_sign * window_size
+            if center_window:
+                end_bound = index[i] + index_growth_sign * window_size/2
+                start_bound = index[i] - index_growth_sign * window_size/2
+            else:
+                end_bound = index[i]
+                start_bound = index[i] - index_growth_sign * window_size
 
             # left endpoint is closed
             if left_closed:
@@ -97,14 +113,27 @@ def calculate_variable_window_bounds(
                     start[i] = j
                     break
 
+            # for centered window advance the end bound until we are
+            # outside the constraint
+            if center_window:
+                for j in range(end[i - 1], num_values+1):
+                    if j == num_values:
+                        end[i] = j
+                    elif ((index[j] - end_bound) * index_growth_sign == 0 and
+                          right_closed):
+                        end[i] = j+1
+                        break
+                    elif (index[j] - end_bound) * index_growth_sign >= 0:
+                        end[i] = j
+                        break
             # end bound is previous end
             # or current index
-            if (index[end[i - 1]] - end_bound) * index_growth_sign <= 0:
+            elif (index[end[i - 1]] - end_bound) * index_growth_sign <= 0:
                 end[i] = i + 1
             else:
                 end[i] = end[i - 1]
 
             # right endpoint is open
-            if not right_closed:
+            if not right_closed and not center_window:
                 end[i] -= 1
     return start, end
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index 558c0eeb0ea65..0b087bebe4e32 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -462,7 +462,9 @@ def _get_window_indexer(self, window: int) -> BaseIndexer:
         if isinstance(self.window, BaseIndexer):
             return self.window
         if self.is_freq_type:
-            return VariableWindowIndexer(index_array=self._on.asi8, window_size=window)
+            return VariableWindowIndexer(
+                index_array=self._on.asi8, window_size=window, center=self.center
+            )
         return FixedWindowIndexer(window_size=window)
 
     def _apply_series(self, homogeneous_func: Callable[..., ArrayLike]) -> "Series":
@@ -470,7 +472,6 @@ def _apply_series(self, homogeneous_func: Callable[..., ArrayLike]) -> "Series":
         Series version of _apply_blockwise
         """
         _, obj = self._create_blocks(self._selected_obj)
-
         try:
             values = self._prep_values(obj.values)
         except (TypeError, NotImplementedError) as err:
@@ -554,7 +555,14 @@ def homogeneous_func(values: np.ndarray):
             if values.size == 0:
                 return values.copy()
 
-            offset = calculate_center_offset(window) if center else 0
+            offset = (
+                calculate_center_offset(window)
+                if center
+                and not isinstance(
+                    self._get_window_indexer(window), VariableWindowIndexer
+                )
+                else 0
+            )
             additional_nans = np.array([np.nan] * offset)
 
             if not is_weighted:
@@ -597,7 +605,9 @@ def calc(x):
             if use_numba_cache:
                 NUMBA_FUNC_CACHE[(kwargs["original_func"], "rolling_apply")] = func
 
-            if center:
+            if center and not isinstance(
+                self._get_window_indexer(window), VariableWindowIndexer
+            ):
                 result = self._center_window(result, window)
 
             return result
@@ -1950,15 +1960,13 @@ def validate(self):
         if (self.obj.empty or self.is_datetimelike) and isinstance(
             self.window, (str, BaseOffset, timedelta)
         ):
-
             self._validate_monotonic()
             freq = self._validate_freq()
 
-            # we don't allow center
-            if self.center:
+            # we don't allow center for offset based windows
+            if self.center and self.obj.empty:
                 raise NotImplementedError(
-                    "center is not implemented for "
-                    "datetimelike and offset based windows"
+                    "center is not implemented for offset based windows"
                 )
 
             # this will raise ValueError on non-fixed freqs