The LIVE-L4 test was conducted to investigate the transient and steady state behavior of the molten pool and the crust influenced by different heat generation rate. In previous work, a simple novel model of the LIVE code was developed to simulate the entire process of the LIVE-L4 test after the melt of KNO3NaNO3 poured into the test vessel. The LIVE code is a transient code and can be used as a fast computational program to simulate the LIVE tests. Calculation results indicated that the LIVE code could generally predict the main parameters of the melt and crust well during the LIVE-L4 test.However, the LIVE code could not predict some processes accurately, such as the early phase of the test after the melt poured into the test vessel, and heat flux distribution at small polar angle, due to no considering the composition change of local melt during the crust formation, which affected the properties of the local melt adjacent to the crust, especially the liquidus temperature of the local melt at the interface of melt and crust. Therefore, considering the effects of the crust growth rate and the diffusion of concentrated NaNO3 on the composition change of the local melt, the diffusion boundary layer (DBL) model was developed and combined with the LIVE code model to consider the composition change of the local melt during the crust formation, with the assumption of considering a quasi-stable plane front solidification of the melt. The DBL-LIVE code was used to calculate the characteristics of the melt and the crust during the heating phase 18 kW. The calculation results indicated that the DBL-LIVE code could predict the main parameters of the melt and crust much more accurately. It could also predict the transient and steady characteristics of the melt composition. Moreover, the thickness of the diffusion boundary layer has a marked influence on the composition distribution. Therefore, the sensitivity analysis of the DBL thickness was also conducted in this work.