Summary: The research studies a class of nonlinear Schrödinger equation with harmonic potential \(\text{i}\varphi_t=-\dfrac12 \varDelta \varphi+\dfrac12 |x|^p\varphi-a|\varphi|^2\varphi-b|\varphi^4|\varphi\), (\(t\geq 0,x\in \mathbb R\), \(p>0\), \(a,b\) is constant). By using energy method, it is proved that if the initial data is satisfied with some conditions, the solutions of equation will blow-up in finite time \(T<\infty\).