Measurements of the magnetoresistance of vanadium carbide have been made as a function of carbon concentration and temperature. For well-ordered samples the results for ${\ensuremath{\rho}}_{1111}$, ${\ensuremath{\rho}}_{1122}$, and ${\ensuremath{\rho}}_{1212}$ are analyzed along with previously taken data for the Hall effect and electrical resistivity. The measurements indicate that an appropriate electronic band structure must include at least two anisotropic (nonspherical) bands for carriers of opposite sign. Comparisons are made to density-of-states data derived from specific-heat measurements and band-structure calculations.