This paper is concerned with the following perturbed elliptic system: − ε 2 △ u + V ( x ) u = W v ( x , u , v ) $-\varepsilon^{2}\triangle u+V(x)u=W_{v}(x, u, v)$ , x ∈ R N , − ε 2 △ v + V ( x ) v = W u ( x , u , v ) $-\varepsilon^{2}\triangle v+V(x)v=W_{u}(x, u, v)$ , x ∈ R N , u , v ∈ H 1 ( R N ) $u, v\in H^{1}({\mathbb{R}}^{N})$ , where V ∈ C ( R N , R ) $V \in C({\mathbb{R}}^{N}, {\mathbb{R}})$ and W ∈ C 1 ( R N × R 2 , R ) $W \in C^{1}({\mathbb{R}}^{N}\times\mathbb{R}^{2}, {\mathbb{R}})$ . Under some mild conditions on the potential V and nonlinearity W, we establish the existence of nontrivial semi-classical solutions via variational methods, provided that 0 < ε ≤ ε 0 , where the bound ε 0 is formulated in terms of N, V, and W.