This paper is concerned with the following semilinear elliptic systems: $$\left \{ \textstyle\begin{array}{@{}l} -\Delta u+V(x)u=H(x)F_{u}(x, u, v), \quad x\in\mathbb{R}^{N}, -\Delta v+V(x)v=H(x)F_{v}(x, u, v), \quad x\in\mathbb{R}^{N}, u(x)\rightarrow0,\qquad v(x)\rightarrow0\quad \mbox{as } |x|\rightarrow\infty, \end{array}\displaystyle \right . $$ where $V(x)$ , $H(x)$ are nonnegative continuous functions. Under some appropriate assumptions on $V(x)$ , $H(x)$ , and $F(x, u, v)$ , we prove the existence of infinitely many small negative-energy solutions by using the fountain theorem established by Zou. Recent results from the literature are extended.