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Abstract By a change of variables with cut-off functions, we study the existence and the asymptotic behavior of positive solutions for a general quasilinear Schrödinger equation which arises from plasma physics. We extend the results of (Adv. Nonlinear Stud. 18(1):131-150, 2017) from α=1 $\alpha=1$ to α>12 $\alpha>\frac{1}{2}$. Especially, we can consider the exponent p in (2,2∗) $(2,2^{*})$ for all N≥3 $N\geq3$.