The application of two-phase computational fluid dynamics (CFD) for simulating crater-like Taylor cone formation dynamics in a viscous liquid is a challenging task. An interface coupled level set/volume-of-fluid (CLSVOF) method and the governing equations based on Navier-Stokes equations were employed to simulate the crater-like Taylor cone formation process. The computational results of the dynamics of crater-like Taylor cone slowly formed on a free liquid surface produced by a submerged nozzle in a viscous liquid were presented in this paper. Some experiments with different air pressures were carried out to evaluate the simulation results. The results from both CFD and experimental observations were compared and analyzed. The numerical results were consistent with the experimental results. Our study showed that the CLSVOF method gave convincing results, and the computational method is robust to extreme variations in interfacial topology.