In this paper, in order to obtain new solutions to nonlinear evolution equations, the auxiliary equation method and (G'/G)-expansion method are studied and extended. By using the method, many new exact solutions of the nonlinear (2+1)-dimensional Nizhnik-Novikov-Vesselov equations with variable coefficients are obtained. The interaction new solutions include Jacobi elliptic function, hyperbolic function, triangular function and rational function.