A numerical procedure for the simulation of diffusional growth in binary and multicomponent alloys has been suggested. The sources of mass balance error in both the representative movable grid and the fixed grid finite difference method were carefully analyzed. Paying attention to the removal or reduction of mass balance error, a new flux balance equation was developed together with a correction of the interface position, based on an explicit fixed grid finite difference method. In the simulation of multicomponent diffusion, a local equilibrium was assumed at the moving interface. The interface compositions were calculated by solving the nonlinear equations which come from a supposition that each solute component should give the same interface moving velocity by the newly developed flux balance equation. The reliability of the present method was demonstrated by comparing the results with the analytical solution or those from phase equilibrium calculation.