A first principles plane-wave method is utilized to investigate the bulk properties of the NiTi alloy，such as the lattice parameters, formation energy and cohesive energy and the elastic constant. The results are in good agreement with experimental and other theoretical results.Furthermore,we have studied the geometric and electronic structures of NiTi (100) and(110)surfaces. As to the surface geometry, there are different relaxations in the surface layers. As for the cleaned NiTi(110) surface, outermost surface layer shows a large rippled relaxation in which Ni atoms contract into the bulk by 0.198? and Ti atoms expand to the vacuum by 0.122?. The calculation of the surface electronic structure shows that Ti-terminated surface is more reactive than Ni-terminated surface on (100) surface and the NiTi (110) surface is inert.