The final result of Fourier velocity mapping is a set of images, each representing the spatial distribution of spins at a given velocity. To acquire data in a short time, the number of encoding gradient steps must be as small as possible, but this can mean sacrificing velocity resolution. We used interpolation methods to obtain high velocity resolution with a small number of encoding steps involving linear interpolation from 16 encoding steps or more and zero-filling interpolation from two to eight encoding steps. Velocity measured by interpolated Fourier-flow encoding agreed well with values obtained using a calibrated phantom. A simulation of noise on the images of the phantom showed that, for a given acquisition time, increasing number of encoding steps in the Fourier flow encoding gave better precision for velocity measurement than did averaging identical signals in phase-mapping methods.