In this paper the electronic densities of states(DOS) of Nb bulk, local densities of states (LDOS) of clean Nb(100) surface and surface energies relative to the bulk have been calculated by using LMTO method. The DOS of bulk Nb calculated in this paper is in agreement well with other method, the calculated surface energies support the result of low energy electron diffraction (LEED)dynamic calculation. Moreover, after analysing the LDOS, we suggest that there are surface states for the clean Nb(100) surface, which are above the Fermi, energy level.