  We consider the final-state problem for the nonlinear Schr\"{o}dinger
equations (NLS) with a suitable time-decaying harmonic oscillator. In this
equation, the power of nonlinearity $|u|^{\rho}u $ is included in the
long-range class if $0 < \rho \leq 2/(n(1- \lambda)) $ with $0 \leq \lambda
<1/2$, which is determined by the harmonic potential and a coefficient of
Laplacian. In this paper, we find the final state for this system and obtain
the decay estimate for asymptotics.
