The simulation of injection molding process requires a stable algorithm to model the molten polymer with non-isothermal non-Newtonian property. In this paper, a staggered and iterative scheme is particularly designed to solve the velocity-pressure-temperature variables. In consideration of the polymer characteristic of high viscosity and low thermal conductivity, the non-Newtonian momentum-mass conservation equations are solved by the Crank-Nicolson method based split (CNBS) scheme, and the energy conservation equation with convective character is discretized by the characteristic Galerkin (CG) method. In addition, an arbitrary Lagrangian Eulerian (ALE) free surface tracking and mesh generation method is introduced to catch the front of the fluid flow. The efficiency of the proposed scheme is demonstrated by numerical experiments including a lid-driven cavity flow problem and an injection molding problem. © 2011 Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg.