The coalescence of viscous liquid drops has been extensively studied due to its wide applications in many industrial processes. With the current advances of high-speed digital camera, a few experimental works have been reported recently. However, the experimental results show discrepancies from both currently available analytical and numerical results. In this study, we present a computational model using finite element method which solves the whole coupled set of continuity and momentum equations governing the hydrodynamics as well as the convection-diffusion equation governing surfactant transport on the interface for the coalescence process of a pendent and a sessile drop. After validating the current model against equilibrium solution, we compared our results with both experimental and analytical results. The transient evolution of the radius of the neck connecting two drops from our simulation agree well with experimental results when the radius is greater than 10% of the original drop radius, which is the lower limit of experimental measurements. In the early stage of coalescence, our results in Stokes region are different from the prediction of theoretical models. The deviation is probably caused by the assumption in theoretical models that coalescence start with a point with infinite velocity instead of a finite initial contact area and zero velocity.