The interface motion in the injection molding process is simulated with the Level Set two-phase flow method，which can avoid both to deal with the complex boundary conditions and to extend the melt velocity to out of the melt boundary by the Ghost method at each time step. The physical governing equation systems are solved by the finite volume method on a non-staggered grid. The Level Set and its reinitialization equation are solved by the finite difference method. Two injection processes，that is the injection process at the horizontal central plane and the vertical central plane of the cavity，are simulated. The influences of different injection velocities，different quantities of the inlets and different Reynolds numbers on the interface motion are studied. The positions of the interface at different time and the pressure distributions when the injection process is over are presented. The features at different stages of the melt motion and how such stages generated are analyzed. The numerical results，which coincide with the experiments，show that when the difference between the width of the injection inlet and that of the mold is not large，if low or middle injection velocities are used，the melt will not break and can be transported steadily to the whole mold cavity. The higher the injection velocity，the shorter the time to reach stable extension flow.