diff --git a/src/mrpro/operators/GrappaOp.py b/src/mrpro/operators/GrappaOp.py
new file mode 100644
index 000000000..ac01f6e49
--- /dev/null
+++ b/src/mrpro/operators/GrappaOp.py
@@ -0,0 +1,138 @@
+from typing import overload
+
+import torch
+from einops import rearrange
+
+from mrpro.data.enums import TrajType
+from mrpro.data.KData import KData
+from mrpro.operators.CartesianSamplingOp import CartesianSamplingOp
+from mrpro.operators.Operator import Operator
+from mrpro.utils.sliding_window import sliding_window
+
+
+class GrappaOp(Operator[torch.Tensor, torch.Tensor]):
+    """GRAPPA operator for filling in missing k-space points."""
+
+    def __init__(
+        self,
+        acs_kdata: KData,
+        sampling_op: CartesianSamplingOp,
+        kernel_size: tuple[int, ...] = (5, 5),
+        grappa_dims: tuple[int, ...] = (-2, -1),
+        regularizer: float = 1e-5,
+    ) -> None:
+        """Initialize a GRAPPA operator.
+
+        Parameters
+        ----------
+        acs_kdata
+            The ACS data to use for GRAPPA. Can be obtained by indexing the aquired KData.
+        sampling_op
+            The sampling operator for the undersampled data. Can be obtaineded by CartesianSamplingOp.from_kdata.
+        kernel_size
+            The size of the kernel to use for GRAPPA.
+        grappa_dims
+            The dimensions to use for GRAPPA.
+        regularizer
+            The regularization parameter for GRAPPA.
+        """
+        super().__init__()
+
+        if not all(acs_kdata.traj.type_along_kzyx[dim] == TrajType.ONGRID for dim in grappa_dims):
+            raise ValueError(f'ACS data for GRAPPA must be Cartesian in dimensions {grappa_dims}.')
+        if len(kernel_size) != len(grappa_dims):
+            raise ValueError('Length of kernel_size must match length of grappa_dims.')
+
+        self.encoding_matrix = acs_kdata.header.encoding_matrix
+        self.grappa_dims = grappa_dims
+        acs_data = acs_kdata.data
+        num_coils = acs_data.shape[-4]
+
+        source_patches = sliding_window(acs_data, window_shape=kernel_size, dim=self.grappa_dims)
+
+        num_features = num_coils * torch.prod(torch.tensor(kernel_size)).item()
+        source_matrix = source_patches.reshape(-1, num_features)
+
+        center_indices = tuple(k // 2 for k in kernel_size)
+        index = (..., slice(None), *tuple([slice(None)] * (source_patches.ndim - acs_data.ndim)), *center_indices)
+        target_matrix = source_patches[index].reshape(-1, num_coils)
+
+        shs = source_matrix.mH @ source_matrix
+        reg_term = regularizer * torch.eye(shs.shape[0], device=shs.device, dtype=shs.dtype)
+        sht = source_matrix.mH @ target_matrix
+        weights = torch.linalg.solve(shs + reg_term, sht)
+
+        self.grappa_kernel = rearrange(weights, '(c_in ...) c_out -> c_out c_in ...', c_in=num_coils).to(acs_data.dtype)
+        self.sampling_op = sampling_op
+
+    def _prepare_for_conv(self, data: torch.Tensor):
+        ndim = data.ndim
+        coil_dim = ndim - 4
+        grappa_dims_pos = [d % ndim for d in self.grappa_dims]
+        other_dims = sorted([d for d in range(ndim) if d not in grappa_dims_pos and d != coil_dim])
+
+        permute_order = (*other_dims, coil_dim, *grappa_dims_pos)
+        permuted_data = data.permute(*permute_order)
+
+        num_other_dims = len(other_dims)
+        if num_other_dims > 0:
+            data_to_conv = permuted_data.flatten(start_dim=0, end_dim=num_other_dims - 1)
+        else:
+            data_to_conv = permuted_data
+
+        original_other_shape = tuple(data.shape[d] for d in other_dims)
+        return data_to_conv, permute_order, original_other_shape
+
+    def _unprepare_from_conv(
+        self,
+        data_conv: torch.Tensor,
+        permute_order: list[int],
+        original_other_shape: tuple[int, ...],
+    ):
+        if len(original_other_shape) > 0:
+            unflattened_data = data_conv.unflatten(0, original_other_shape)
+        else:
+            unflattened_data = data_conv
+
+        inverse_permute_order = torch.argsort(torch.tensor(permute_order))
+        return unflattened_data.permute(*inverse_permute_order)
+
+    @overload
+    def forward(self, data: torch.Tensor) -> tuple[torch.Tensor,]: ...
+
+    @overload
+    def forward(self, data: KData) -> KData: ...
+
+    def forward(self, data: torch.Tensor | KData) -> tuple[torch.Tensor,] | KData:
+        """Apply GRAPPA to the data, i.e. fill in the missing data points.
+
+        Parameters
+        ----------
+        data
+            The data to apply GRAPPA to.
+        """
+        if isinstance(data, KData):
+            (gridded_data,) = self.sampling_op.adjoint(data.data)
+        else:
+            (gridded_data,) = self.sampling_op.adjoint(data)
+
+        (
+            data_to_conv,
+            permute_order,
+            original_other_shape,
+        ) = self._prepare_for_conv(gridded_data)
+
+        conv_fn = (torch.nn.functional.conv1d, torch.nn.functional.conv2d, torch.nn.functional.conv3d)[
+            len(self.grappa_dims) - 1
+        ]
+        synthesized_flat = conv_fn(data_to_conv, self.grappa_kernel, padding='same')
+        synthesized_data = self._unprepare_from_conv(synthesized_flat, permute_order, original_other_shape)
+
+        (masked_synthesized,) = self.sampling_op.gram(synthesized_data)
+        reconstructed_data = gridded_data + synthesized_data - masked_synthesized
+
+        if isinstance(data, KData):
+            header = data.header.clone()
+            full_traj = self.sampling_op.full_trajectory()
+            return KData(header=header, data=reconstructed_data, traj=full_traj)
+        return (reconstructed_data,)