The band structures and effective masses of III-V semiconductors InP, InAs, InSb, GaAs, and GaSb are calculated using the GW method, the Heyd, Scuseria, and Ernzerhof hybrid functional, and modified Becke-Johnson combined with the local-density approximation MBJLDA—a local potential optimized for the de-scription of the fundamental band gaps F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 2009. We find that MBJLDA yields an excellent description of the band gaps at high-symmetry points, on par with the hybrid functional and GW. However, the effective masses are generally overestimated by 20– 30 % using the MB-JLDA local multiplicative potential. We believe this to be related to incorrect nearest-neighbor hopping ele-ments, which are little affected by the choice of the local potential. Despite these shortcomings, the MBJLDA method might be a suitable approach for predicting or interpolating the full band dispersion, if only limited experimental data are available. Furthermore, the method is applicable to systems containing several thousand atoms where accurate quasiparticle methods are not applicable.