In this paper we study the following nonlinear Schrodinger system:

Here, $a,\,b,\,\lambda\in C(\mathbb R^N,\,\mathbb R)$ are all non-periodic in $x_i$ for $i=1,\,\cdots,\,N$, $N\geq 3$,  $f,\,g\in C(\mathbb R^2,\,\mathbb R)$. We show that this system has infinitely many solutions with small negative energies  and infinitely many  large-energy  solutions. To the best of our knowledge, there is no corresponding result about such a  Schrodinger system.