Abstract: Numerical simulations of the filling process of injection molding for polymer are implemented on a 3D complex cavity with uneven thickness. The domain-extension method is used to deal with boundary of complex cavity, a two-phase flow model is proposed, in which the Navier-Stokes equation and Level Set equation are coupled. The equations are discretized by the finite volume method and solved by the SIMPLE algorithm on the collocated mesh. Based on the model and algorithm above mentioned, the evolution of front interface and flow of polymer melt in the complex cavity are predicted successfully, and the "speedway" phenomenon and "fountain flow" phenomenon in this cavity with uneven thickness are captured. Numerical results show that the domain-extension method combined with finite volume method is effective, and can be used to simulate the filling process of polymer melt in a relatively complex cavity.