In this paper, we study the following quasilinear Schrödinger equation −∆u + V(x)u − [∆(1 + u 2) 1/2 ] u 2(1 + u 2) 1/2 = h(u), x ∈ R N , where N ≥ 3, 2 * = 2N N−2 , V(x) is a potential function. Unlike V ∈ C 2 (R N), we only need to assume that V ∈ C 1 (R N). By using a change of variable, we prove the non-existence of ground state solutions with Berestycki-Lions conditions, which contain the superliner case: lim s→+∞ h(s) s = +∞ and asymptotically linear case: lim s→+∞ h(s) s = η. Our results extend and complement the results in related literature.