Authors’ abstract: We study the following singularly perturbed problem for a coupled nonlinear Schrödinger system which arises in Bose-Einstein condensate: \(-{\epsilon}^{2}{\Delta}u + a(x)u = {\mu}_{1}u^{3} + {\beta}uv^{2}\) and \(-{\epsilon}^{2}{\Delta}v + b(x)v = {\mu}_{2}v^{3} + {\beta}u^{2}v\) in \(\mathbb {R}^3\) with \(u, v > 0\) and \(u(x), v(x) \to 0\) as \(|x| \to \infty\) . Here, \(a\), \(b\) are non-negative continuous potentials, and \({\mu}_{1}, {\mu}_{2} > 0\). We consider the case where the coupling constant \({\beta} > 0\) is relatively large. Then for sufficiently small \(\varepsilon > 0\), we obtain positive solutions of this system which concentrate around local minima of the potentials as \(\varepsilon \to 0\). The novelty is that the potentials \(a\) and \(b\) may vanish at someplace and decay to 0 at infinity.