The electronic stucture of three kinds of MoSi2(001)surface with C11b crystal structure were studied by using LMTO一ASA method, their surface total electronic densities of states and local densities of states of surface layer as well as partial densities of states, were provided and compared with the correlated atomic bulk densities of states. As to the stability of the surfaces, the densities of states on Fermi level's were discussed, the Si monolayer surface is the most stable one among them, which support the experimental results obtained by Kemoda et al.