Effect of salt concentration on the rheology behavior of Laponite suspension was investigated with large amplitude oscillatory shear(LAOS) rheology. Nonlinear viscoelasticity of Laponite suspensions was demonstrated by the related amplitude I-3/1, the minimum-strain modulus(G(M)), large-strain modulus(G(L)), minimum-strain rate viscosity (eta(M)), and large-strain rate viscosity (eta(L)). I-3/1 increased gradually with gamma(0) for the samples with low NaCl concentration. As the concentration of NaCl increased, I-3/1 increased abruptly with gamma(0) and reached a plateau value. The relationship of G(M) and G(L) parameters with gamma(0) showed no difference among samples with different NaCl concentrations. The eta(M) and eta(L) parameters exhibited a large peak in the relationship with gamma(0), which differed significantly among samples with different NaCl concentrations. The higher the NaCl concentration was, the higher the peak value was. These results suggested that the nonlinear viscoelasticity of Laponite gels depended on their network structure. By increasing NaCl concentration, the electrostatic interaction between Laponite particles was screened and the distance between Laponite particles was reduced, leading to a more condensed gel network. This network was easily broken under LAOS, showing obvious nonlinear viscoelasticity.