In order to inject gas into a heavy oil reservoir, molecular diffusion of the dissolved gas into heavy oil is one of the crucial mechanisms to lower its viscosity while swelling the diluted oil. Various efforts have been made to predict the diffusivity of such gas dissolved in heavy oil with or without considering the oil swelling. Practically, the oil swelling is always considered in an excessively simplified manner so that such swelling is not able to exhibit its true effect on the estimated diffusivity. In most studies where the oil swelling is considered, the liquid-phase hydrocarbon is assumed to swell equally at every location because the height of liquid-phase in a diffusion vessel is simply extended proportionally to the oil swelling direction. Such a proportional swell is often realized during numerical solutions by uniformly extending the numerical cells, regardless of the amount of dissolved gas contained in each of them. In addition, no studies have been made to examine the contribution of one gas over the other for a gas mixture-liquid system. In this study, a pragmatic approach is proposed to determine the main- and cross-term diffusivities of gas-liquid systems considering local swelling effect. More specifically, diffusivities of CO2 and a CO2-C3H8 mixture in a Lloydminster heavy oil are respectively estimated by implementing the finite difference approximation (FDA) with the face-centered explicit scheme. For the CO2-C3H8 mixture, the individual diffusivity of each gas in the mixture is firstly computed independent of the other gas in the mixture. Then, the cross-term diffusivity is included to verify the effect of the other gas in heavy oil for the diffusion of one gas, while the local oil swelling is implemented during the estimation of the individual gas diffusivities. It is found that the obtained diffusivities of pure CO2 and each individual component of the CO2-C3H8 mixture in the Lloydminster heavy oil are reasonable and accurate to reproduce the measured oil swelling factors obtained from the dynamic volume analysis (DVA) tests.