In this paper we study the existence of nontrivial classical solution forthe quasilinear Schr\"odinger equation: −Δu+V(x)u+2κΔ(u2)u=f(u),%in RN, where N≥3, f hassubcritical growth and V is a nonnegative potential. For this purpose, we use variational methods combined with perturbation arguments, penalization technics of Del Pino and Felmer and Moser iteration. As a main novelty with respect to some previous results, in our work we are able to deal with the case \kappa > 0 and the potential can vanish at infinity