A gas-liquid two-phase model for the simulation of viscoelastic fluid mold filling process with the consideration of phase change is proposed, in which the governing equations for the melt and air in the cavity, including the mass conservation, momentum conservation and energy conservation equations, are unified into one system of equations. A revised enthalpy method, which can be used for both the melt and air in the mold cavity, is proposed to describe the phase change during the mold filling. Finite volume method on non-staggered grid is used to solve the system. The level set method is used to capture the interface evolution in the mold filling process. The distributions of physical quantities such as velocity, pressure and temperature and so on are given. The "frozen skin" layers under different temperatures and velocities are discussed in detail. Numerical results show that increasing the temperatures of the melt and cavity is a better way to get rid of the "frozen skin" layer than increasing the injection velocity.