Numerical simulation of transient mass transfer to a single drop controlled by the internal resistance or by the resistance in both phases was mathematically formulated and simulated in a boundary-fitted orthogonal coordinate system. The simulated results on the transient mass transfer dominated by the internal resistance are in good agreement with the Newman and Kronig-Brink models for drops with low Reynolds number. When the drop Reynolds number is up to 200, the mass transfer coefficient from numerical simulation is very low as compared with the Handlos-Baron model. The cases with mass transfer resistance residing in both the continuous and drop phases were simulated successfully and compared with the experimental data in three extraction systems recommended by European Confederation of Chemical Engineering (EFCE). For single drops with Re < 200, the numerically predicted values of the extraction fraction and overall mass transfer coefficient are in reasonable coincidence with the experimental data. It is concluded that the numerical simulation can be resorted in some cases of solvent extraction for conducting numerical experiments and parametric study. Nevertheless, for better resolution as higher Reynolds number drops are simulated, more sophisticated techniques should be developed and incorporated to deal with the large deformation and transient shape oscillation as well as possible Marangoni effect.