A mass transfer model is developed using the volume-of-fluid (VOF) method with a piecewise linear interface calculation (PLIC) scheme in ANSYS FLUENT for a free-rising bubble. The mass flow rate is defined via the interface by Fick's law and added into the species equation as a source term in the liquid phase using the user-defined functions (UDFs) in ANSYS FLUENT. The interfacial concentration field for the mass flow rate is discretized by two numerical methods. One of them is based on the calculation of the discretization length between the centroid of the liquid volume and the interface using the liquid void fraction and interface normal vectors at the interface cells, while in the second method the discretization length is approximated using only the liquid void fraction at the interface cells. The influence of mesh size, schemes, and different Schmidt numbers on the mass transfer mechanism is numerically investigated for a free-rising bubble. Comparison of the developed mass transfer model with the theoretical results shows reasonable and consistent results with a smaller time-step size and with cell size.