In this work, an improved simple coupled level-set and volume of fluid (S-CLSVOF) method is proposed to trace the moving interfaces in gas assisted injection moulding (GAIM) process based on the viscoelastic FENE-P model. Firstly, the Kreisselmeier-Steinhauser (KS) function constructed by means of Boolean operations is adopted as the shape level set (LS) function to precisely represent the complex mould cavities. Then, the benchmark problem of two-dimensional deformation is used to verify the ability of the S-CLSVOF method for capturing the moving interfaces. The stress birefringence is calculated and compared with the experiment result. Finally, the proposed method is further applied to the mould filling and gas penetration processes in GAIM. The macroscopic bubble appearance, temperature distribution, and the behaviour of the mesoscopic molecular orientation are shown and analyzed in detail. Due to the complexity of the gas-liquid interaction, the phenomenon of asymmetrical gas flow is clearly observed in the gas penetration process. The influences of the macroscopic parameters on the macroscopic gas flows and mesoscopic molecular orientation are also discussed, such as insert positions, melt temperatures, and gas delay time. The numerical results illustrate that the coupled method can be applied to the multiscale numerical simulation of viscoelastic flows with complex free surfaces and provide significant guidance for the GAIM process.