The resonance problem of a quasilinear elliptic equation with superlinear nonlinearities were focused.By establishing the relationship between the quasilinear operators and linear operators, according to the Shapiro-type compact embedding theorem and Brouwer's theorem, the existence of solutions of the approximate equation was revealed.With the help of the Sobolev theory, Fatou's Lemma and Lebesgue dominated convergence theorem, the uniform boundness of the approximate solutions was proved.By using the projection technique and the Galerkin method, the existence of nontrivial solutions of the resonance problem was revealed.