The electronic structure of stoichiometric vanadium carbide has been computed using the augmented-plane-wave (APW) method and the energy bands for nonstoichiometric phases have been determined with the APW---virtual-crystal approximation. The energy bands exhibit a very strong dependence on the relative sizes of the assumed APW-sphere radii for vanadium and carbon. Bands for the nonstoichiometric phases show a marked deviation from a rigid-band behavior as the composition is varied. The results of x-ray-emission, heat-capacity, magnetic-susceptibility, and Hall-effect measurements are discussed in terms of the computed bands.