  We investigate the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta
u+|u|^{p-1}u=0$ with $1+\frac{4}{N}<p<1+\frac{4}{N-2}$ (when $N=1, 2$,
$1+\frac{4}{N}<p<\infty$) in energy space $H^1$ and study the divergent
property of infinite-variance and nonradial solutions. If
$M(u)^{\frac{1-s_{c}}{s_{c}}}E(u)<M(Q)^{\frac{1-s_{c}}{s_{c}}}E(Q)$ and
$\|u_{0}\|_{2}^{\frac{1-s_{c}}{s_{c}}}\|\nabla
u_{0}\|_{2}>\|Q\|_{2}^{\frac{1-s_{c}}{s_{c}}}\|\nabla Q\|_{2},$ then either
$u(t)$~blows up in finite forward time, or $u(t)$ exists globally for positive
time and there exists a time sequence $t_{n}\rightarrow+\infty$ such that
$\|\nabla u(t_{n})\|_{2}\rightarrow+\infty.$ Here $Q$ is the ground state
solution of $-Q+\Delta Q+|Q|^{p-1}Q=0.$ A similar result holds for negative
time. This extend the result of the 3D cubic Schr\"{o}dinger equation in
\cite{holmer10} to the general mass-supercritical and energy-subcritical case .
