We studied the asymptotic behavior of sol utions to the initial boundary value problem on the spatial interval [0,1] for a one-dimensional simplified gydrodynamic model for semiconductors when g(t)→b*, and proved the unique global existence of smooth solutions to the initial boundary problem. We also show that the solutions converge to the corre sponding steady-state solutions time-asymptotically by introducing the suitabl e shift functions.