  We consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation $i
\partial_{t}u+ \Delta u=\lambda_{0}u+\lambda_{1}|u|^\alpha u$ in
$\mathbb{R}^{N}$, where $\lambda_{0},\lambda_{1}\in\mathbb{C}$, in $H^s$
subcritical and critical case: $0<\alpha\leq\frac{4}{N-2s}$ when
$1<s<\frac{N}{2}$ and $0<\alpha<+\infty$ when $s\geq\frac{N}{2}$. We show that
the solution depends continuously on the initial value in the standard sense in
$H^{s}(\mathbb{R}^{N})$ if $\alpha$ satisfies certain assumptions.
