The formation of a vapor cloud following the spill of cryogenic hazardous liquid on ground presents significant fire or toxic hazards. Predicting the evaporation rate is central for risk assessment purpose to estimate the consequences of the cryogenic liquid spill. Numerical simulation is performed to study the heat transfer from the ground to the liquid pool during the vaporization process. Sensitivity analysis is carried out and a set of optimized simulation parameters with a domain size of 0.2 m, a space resolution of 0.2 mm, and a time resolution of 20 ms is chosen. The effect of different boiling modes on the heat transfer is further studied using a boiling curve to specify the boundary condition. Three different boiling stages - film boiling, transition boiling and nucleate boiling - are identified. The heat flux across the ground surface to the liquid pool is discussed during the whole cooling process following the cryogenic liquid spill on the ground. The ability of this numerical model to consider complex boiling phenomena is encouraging as its further development would potentially provide an accurate description of the source term model of vapor formation during cryogenic liquid spill.