Severe stenosis may cause critical flow conditions related to artery collapse, plaque cap rupture which leads directly to stroke and heart attack. In this paper, a nonlinear viscoelastic model and a numerical method are introduced to study dynamic behaviors of the tube wall and viscous flow through a viscoelastic tube with a stenosis simulating blood flow in human carotid arteries. The Mooney-Rivlin material model is used to derive a nonlinear viscoelastic thin-wall model for the stenotic viscoelastic tube wall. The mechanical parameters in the Mooney-Rivlin model are calculated from experimental measurements. Incompressible Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation are used as the governing equation for the fluid flow. Interactions between fluid flow and the viscoelastic axisymmetric tube wall are handled by an incremental boundary iteration method. A Generalized Finite Differences Method (GFD) is used to solve the fluid model. The Fourth-Order Runge-Kutta method is used to deal with the viscoelastic wall model where the viscoelastic parameter is adjusted to match experimental measurements. Our result shows that viscoelasticity of tube wall causes considerable phase lag between the tube radius and input pressure. Severe stenosis causes cyclic pressure changes at the throat of the stenosis, cyclic tube compression and expansions, and shear stress change directions in the region just distal to stenosis under unsteady conditions. Results from our nonlinear viscoelastic wall model are compared with results from previous elastic wall model and experimental data. Clear improvements of our viscoelastic model over previous elastic model were found in simulating the phase lag between the pressure and wall motion as observed in experiments. Numerical solutions are compared with both stationary and dynamic experimental results. Mooney-Rivlin model with proper parameters fits the non-linear experimental stress-strain relationship of wall very well. The phase lags of tube wall motion, flow rate variations with respect to the imposed pulsating pressure are simulated well by choosing the viscoelastic parameter properly. Agreement between numerical results and experimental results is improved over the previous elastic model.