In this paper, we are concerned with the following coupled Schrödinger equations − λ 2 Δ u + a 1 x u = c x v + a 2 x u p − 2 u + a 3 x u 2 ∗ − 2 u , x ∈ ℝ N , − λ 2 Δ v + b 1 x v = c x u + b 2 x v p − 2 v + b 3 x v 2 ∗ − 2 v , x ∈ ℝ N , where 2 p 2 ∗ , 2 q 2 ∗ , 2 ∗ = 2 N / N − 2 , and N ≥ 3 ; λ > 0 is a parameter; and a 1 , a 2 , a 3 , b 1 , b 2 , b 3 , c ∈ C ℝ N , ℝ and u , v ∈ H 1 ℝ N . Under some suitable conditions that a 1 0 = inf a 1 = 0 or b 1 0 = inf b 1 = 0 and c x 2 ≤ ϑ a 1 x b 1 x with ϑ ∈ 0 , 1 , the above coupled Schrödinger system possesses nontrivial solutions if λ ∈ 0 , λ 0 , where λ 0 is related to a 1 , a 2 , a 3 , b 1 , b 2 , b 3 , and N .