In this paper an R-function is employed to construct the shape level set (LS) function for representing the complex mould cavity in a gas-assisted injection moulding (GAIM) process. With the shape LS function, the continuity, momentum, and energy equations can be extended for solving the gas-liquid two-phase flows using the finite volume and immersed boundary methods. Firstly, an improved simple coupled level set and volume of fluid (S-CLSVOF) method is proposed to track the moving interfaces of gas-liquid interface and polymer melt front. Then the benchmark problems of the two- and three-dimensional deformation tests are carried out to verify the ability of the improved S-CLSVOF method. At last, the gas penetration processes are simulated in two different complex mould cavities. The numerical results show that the improved S-CLSVOF method has higher accuracy than the S-CLSVOF method, and the coupled numerical framework can successfully depict the asymmetry phenomenon of gas flow, racetracking, and fountain phenomena, which has great significance in determining processing conditions and designing mould cavities.