We have calculated the atomic and electronic structures of the non-polar surface of GaN(1010) by employing the full potential augmented plan wave and local orbital method (APW+lo). The calculated lattice constant and bulk modulus of zinc-blend GaN crystal are in excellent agreement with the experimental dat a. Using the slab and supercell model, we find that the surfae is characterized by a top-layer bond-lenth-contracting rotation relaxation. The surface Ga atom moves inward with 0014nm and form a planar sp2-like bonding with its three N neighbors. While the surface N atom moves outward with 0013nm and tends to a taper p3-like bonding with its three Ga neighbors. The surface layer rotation angle is 85°. From the calculated results of the desity of states of GaN (1010) surface we find that the surface relaxation induces the transformation from s emi-metallic to semi- conducting characteristic. Furthermore, it is also shown t hat the surface charges have a large transfer, and the surface bonds have a rehy bridization, which makes the ionicity reduce and the covalence increase, we beli eve that it causes the surface bond shortening and rotating.