First-principle calculations based on the plane-wave pseudopotential method have been used to study the surface energy and structure of anatase TiO2(101) surface.There are six different structures of the anatase TiO2(101) crystal surface because different atoms are terminated on the surface layers. The calculation result shows that anatase TiO2(101) crystal surface structure which the outermost and second layer respectively terminated by twofold coordinated oxygen atoms and fivefold coordinated titanium atoms is much more stable than the other five structures. By investigating the effect of variable vacuum layer thickness and slab thickness on the surface energy and surface atomic displacements, we find that slab thicknesses of at least 12 atom layers and vacuum layer thickness of more 0.4nm are sufficient to converge the surface energy to within 0.01 J/m2. At last, we obtained the result that the twofold coordinated oxygen atoms have an inward relaxation of 0.0012nm, and fivefold coordinated titanium atoms have an outward relaxation of 0.0155nm,while the length of Ti—O bonds and quantity of electric charge of titanium and oxygen atoms are changed, making the structure more stable.