  We consider the nonlinear Schr\"{o}dinger equation with $L^{2}$-supercritical
and $H^{1}$-subcritical power type nonlinearity. Duyckaerts and Roudenko and
Campos, Farah, and Roudenko studied the global dynamics of the solutions with
same mass and energy as that of the ground state. In these papers, finite
variance is assumed to show the finite time blow-up. In the present paper, we
remove the finite-variance assumption and prove a blow-up or grow-up result.
