  In this paper we consider the transverse instability for a nonlinear
Schr\"odinger equation with a linear potential on $\mathbb{R} \times
\mathbb{T}_L$, where $2\pi L$ is the period of the torus $\mathbb{T}_L$. Rose
and Weinstein showed the existence of a stable standing wave for a nonlinear
Schr\"odinger equation with a linear potential. We regard the standing wave of
nonlinear Schr\"odinger equation on $\mathbb{R}$ as a line standing wave of
nonlinear Schr\"odinger equation on $\mathbb{R} \times \mathbb{T}_L$. We show
the stability of line standing waves for all $L>0$.
