We consider the following quasilinear Schrodinger system in $${\mathbb{R}^N}$$ with $${N\geq3}$$ : P $$\left\{\begin{array}{l}\sum_{i,j=1}^{N}D_j(a_{ij}(u)D_i u)-\frac{1}{2} \sum_{i,j=1}^{N}D_s a_{ij}(u) D_i u D_j u-A(x) u+F_u(u,v)=0 \\ \sum_{i,j=1}^{N}D_j(a_{ij}(v)D_iv)-\frac{1}{2} \sum_{i,j=1}^{N}D_s a_{ij}(v) D_i v D_j v-B(x)v+F_v(u,v)=0,\end{array} \right.$$ where $${D_i=\frac{\partial}{\partial x_i},\ \ D_s a_{ij}(s)=\frac{d}{ds}a_{ij}(s)}$$ , $${F(u,v)}$$ is the coupling term, $${A(x)}$$ and $${B(x)}$$ are finite and sign-changing potential functions. Using an approximation scheme and $${q}$$ -Laplacian regularization, we prove the existence of infinitely many solutions for system $${(P)}$$ .