The generation of spin current in a one dimensional electron gas (1DEG) system is studied, where the Rashba spin-orbit coupling (RSOC) is modulated by a time-varying gate voltage. With a simple unitary transformation, we show the appearance of an additional spin-dependent potential which results in a spin-dependent effective electric field. We include the scattering interaction by taking a relaxation approximation. The formula for the induced spin current is derived, the limit value accessible by time-varying RSOC is obtained and the order of magnitude is estimated. We find that the maximum of a pulsed spin current can reach that limit value. The results in 1DEG are extended to 2DEG. In addition, we study the spin current in a metal-quantum dot-metal system.