We have studied the equilibrium lattice constants and energy band structures of NbC and NbN using the full-potential linearized augmented-plane-wave (FP-LAPW) method within the framework of the density functional theory (DFT). The calculation has been performed by using the generalized gradient approximation (GGA) for the exchange and correlation potential. Computations have been performed using the WIEN2k codes. The result obtained is reasonable and compares well with the experimental data and other calculations.