For the following elliptic system in R 3 − ε 2 Δ v + V ( x ) v + ϕ ( x ) v = f ( v ) , − Δ ϕ = v 2 , lim | x | → ∞ ϕ ( x ) = 0 , we construct positive solutions u and ϕ which concentrate at several given isolated local minimum components of V as ε → 0 . The potential V is a strictly positive continuous function and the nonlinearity f is subcritical near infinity and superlinear near zero and satisfies only the Berestycki–Lions condition.