Numerical simulations have been carried out for laminar sinusoidal pulsating flow in a tube with smooth single constriction. A second-order finite volume method has been developed to solve the fluid flow governing equations on a nonstaggered non-orthogonal grid. The effects of the Reynolds number, the Womersley number, the pulsatile amplitude, the constriction ratio and the constriction length on fluid flow in constricted tube will be investigated. It will be demonstrated that the dynamic nature of the pulsating flow greatly depends on the frequency of the flow changes. It is observed that the peak wall vorticity seems to increase with the increase of Reynolds number, the pulsating amplitude and the constriction ratio. The peak values of instantaneous wall vorticity are not greatly affected by the variation of Womersly number. The constriction length does not put a significant impact on the flow instantaneous streamline behaviors compared with other parameters. However, the peak wall vorticity increases monotonically with the decrease of the constriction length.