Abstract: Stabilized fractional step algorithm has been widelyaccepted for numerical solution of the incompressible N-S equations. Basedon Guermond's works, the stability of the fractional step algorithm requiresthat the time step size should be larger than a critical value. However, inmodeling of high-viscosity fluid flows, existing explicit and semi-implicitversions of the algorithm require to use smaller time step sizes due totheir explicit nature, which reduces the efficiency of the numericalsolution procedure and very often conflicts with the minimum time step sizerequirement presented to ensure the stability of the fractional stepalgorithm. The purpose of this paper is to present a modified version of thefractional step algorithm, which allows much larger time step sizes thanthose for the preceding ones. The method is based on introducing aniteration algorithm. Numerical experiments in the cavity flow and the planePoisseuille flow problems demonstrate the improved performance of theproposed modified version of the fractional step algorithm, which is furthersuccessfully applied to numerical simulation of the polymer injectionmolding process with high efficiency.