The functionality and performance of the electronic product are heavily dependent on its quality of power device and radio frequency device, thus further determined by the quality of SiC substrate. Hence, the manufacturing of superior SiC single crystal is of significant importance. One popular way of growing large-diameter SiC single crystal is to leverage physical vapor transport (PVT) method. However, this method admits a common challenge in thermal design and flow control. To tackle this problem, a numerical simulation study of the complete process of growing 150 mm SiC single crystal by resistive heating PVT method was proposed in this paper. A mathematical model to capture the growing process, which comprises the pyrolysis and recrystallization of source materials, the porous structure evolution, the heat-mass transport in the system, and the morphology changes of crystal growth front was established. In order to validate our developed model, the numerical simulations were implemented to study the interaction among the crystal growth, the consumption of source materials, and the thermal field changes. The results show that the high temperature on the side of the source area leads to uneven gas flow, and the high temperature at the bottom results in a uniform airflow and a slightly convex crystal surface. Meanwhile, the growth interface adjusts the equilibrium pressure of the gas species through the radial temperature distribution, therefore, the crystal surface grows into an isotherm shape. In addition, the crystal growth rate is positively correlated with the temperature of the source area and the amount of remaining raw materials. The simulation results are consistent with the reported experimental results inherently, which lay a solid foundation for the optimal growth of large-scale and high-quality SiC single crystals.