The level set method is combined with the concentration transformation method to solve the interphase mass transfer process. However, the artificial diffusion generated in the mass transfer convection term across the interface is inevitable, especially when large shape deformation is encountered at high Reynolds numbers. A semi-Lagrangian advection scheme is introduced to overcome this disadvantage. The methyl isobutyl ketone (MIBK)-acetic acid-water system is adopted to study the unsteady mass transport process accompanied with the Marangoni effect of a single deformable drop ascending in the infinite continuous phase. The predicted overall mass transfer coefficients agree with experimental data very well. The configuration of Marangoni convection is revealed and its effect on the interphase mass transfer process is investigated.