Three-dimensional cell models are constructed for fast ionic conductor AgxTiS2 according to the two-dimensional ordered structure of Ag+ ion-vacancy. Geometry optimization and total energy computation are performed for ordered AgxTiS2(x=0，1/4，1/3，1/2，2/3，3/4，1)series using plane-wave pseudo-potential method based on local density approximation to density-functional theory, and the results are compared with the LixTiS2 series. The increments of lattice parameters Δa0 and Δc0 increase monotonically with increasing ion concentration, which well accords with experimental results. The total energies of AgxTiS2 and LixTiS2 system decrease linearly with increasing ion concentration, and the former decreases more rapidly. The negative formation energies of AgxTiS2(x=1/4, 1/3, 1/2, 2/3, 3/4)system indicate their ground state property, among which the formation energy of Ag1/3TiS2 system with 31/2a0×31/2a0 superstructure is the lowest. The formation energy of ordered AgxTiS2(x=1/4, 1/3, 1/2, 2/3, 3/4)system is lower than that of LixTiS2 system, implying higher temperature of order-disorder transition and higher activation energy of ionic diffusion. Reasonable explanation for related experimental results are presented according to these computational results.