  We study the instability of standing-wave solutions $e^{i\omega
t}\phi_{\omega}(x)$ to the inhomogeneous nonlinear Schr\"{o}dinger equation
$$i\phi_t=-\triangle\phi+|x|^2\phi-|x|^b|\phi|^{p-1}\phi, \qquad
\in\mathbb{R}^N, $$ where $ b > 0 $ and $ \phi_{\omega} $ is a ground-state
solution. The results of the instability of standing-wave solutions reveal a
balance between the frequency $\omega $ of wave and the power of nonlinearity
$p $ for any fixed $ b > 0. $
