By establishing a relationship between the quasilinear operator M and the linear operator L,and making reasonable assumptions about nonlinear terms,the existence of a nontrivial solution for a class of quasilinear elliptic equations with high eigenvalues in a weighted Sobolev space was proved.The proof relies on the Galerkin method,the Brouwer′s theorem and a new weighted compact Sobolev type embedding theorem established by Shapiro.