Because of the relatively small size of vessels and limited magnetic resonance (MR) imaging resolution, the accuracy of volume flow rate measurements is limited. A technique that corrects the partial-volume effect in volume flow rate measurements is presented. The technique uses small-phase-shift approximation, with the assumption that blood flow in the voxels at the boundary of the vessel is slow. With the proposed correction technique, the volume flow rate in partially occupied voxels is corrected on a voxel-by-voxel basis and the accuracy of flow measurements increases. Results are shown analytically and for MR phantom data.