The geometry and electronic structure of PbTe(001) surface are calculated using the density functional theory method. It is shown that the (001) surface has no reconstruction and exhibits a significant oscillatory geometric relaxation. The top-to-second layer distance contracts by 4.5% and the second-to-third layer dis tance expands by near 2.0%. In addition, the surface shows a strong rumpling. Th e electronic structure of PbTe(001) surface differs from that of the bulk. With respect to the bulk energy gap at the L point, the surface energy gap broadens a t the X point. The surface states or resonance states are localized mainly near the top of the valence band and the bottom of the conduction band, while there a re no new surface states appearing in the fundamental energy gap. The density of state at Fermi level of the relaxed structure of PbTe(001) surface is very low, thus it is very stable.