Summary: We study the stability of standing waves \(e^{i\omega t}\phi_\omega(x)\) for a nonlinear Schrödinger equation \[ i\partial_t u= -\Delta u+ V(x)u-|u|^{p-1}u,\quad (t,x)\in\mathbb{R}^{1+ n}, \] with an attractive power nonlinearity \(|u|^{p-1}u\) and a potential \(V(x)\) in \(\mathbb{R}^n\). Here, \(\omega\in\mathbb{R}\) and \(\phi_\omega(x)\) is a ground state of the stationary problem. Under suitable assumptions on \(V(x)\), we show that \(e^{i\omega t}\phi_\omega(x)\) is stable for \(p< 1+4/n\) and sufficiently large \(\omega\), or for \(1< p< 2^*-1\) and \(\omega\) close to \(-\lambda_1\), where \(\lambda_1\) is the lowest eigenvalue of the operator \(-\Delta+ V(x)\). We give an improvement of previous results such as H. A. Rose and M. I. Weinstein [Physica D. 30, 207-218 (1988; Zbl 0694.35202)] or M. Grillakis, J. Shatah and W. Strauss [J. Funct. Anal. 74, 160-197 (1987; Zbl 0656.35122)] for unbounded potentials \(V(x)\) which cannot be treated by the standard perturbation argument.