Mass transfer plays a key role in affecting the efficiency of solvent-based processes in enhanced oil recovery. The mass transfer is usually very slow because of the pure molecular diffusion. However, it can be greatly enhanced by frontal instability when solvent is injected to displace oil. Under unfavorable mobility contrast, the interface between two fluids May become very convoluted as displacements continue. This therefore increases the contact area and leads to more efficient mixing. It is necessary to accurately simulate the detailed frontal instability and its propagation with time in order to investigate its effect on the mass transfer. Most of previous numerical simulations assumed a constant diffusion coefficient (CDC) in solvent-based processes. However, experimental studies on the mixing between two miscible fluids indicated that the diffusion coefficients actually vary with concentration or viscosity. Moreover, some numerical simulations with commercial simulators also showed that using the CDC May result in very high and unrealistic values when matching the oil production rate. In present study, a concentration-dependent diffusion coefficient (CDDC) is considered in which the diffusion coefficient is exponentially proportional to concentration. Highly accurate nonlinear numerical simulations are conducted to simulate the frontal instability under unfavorable mobility ratio between solvent and oil. The effect of injection rate and mobility contrast on frontal instability and mass transfer is examined, and the breakthrough time for the CDDC case is discussed. For better comparisons, the CDC case is presented to more clearly show the effects of CDDC.