A transient sessile droplet evaporation numerical model based on Arbitrary-Lagrangian-Eulerian (ALE) formulation is developed, taking into account of the coupled transport processes in solid, liquid and gas phases as well as the evolution of free surface. The ALE formulation can trace the sharp two-phase interface and therefore can calculate evaporative flux and surface tension force accurately. The numerical simulations of axisymmetric sessile droplets evaporation at fixed contact line mode are conducted to verify the numerical model by comparing with the previous quasi-steady-state numerical simulation results and experimental data. It is shown that the present numerical model can predict the evaporation rate at quasi-steady-state, the droplet surface temperature distribution and the droplet volume variation with time correctly. The importance of evaporative cooling is emphasized and the influence of Marangoni flow on evaporation rate and surface temperature distribution are analyzed under different contact angles. The numerical model developed in this study can easily be extended to simulate more complicated droplet evaporation situations, such as contact line dynamics during droplet evaporation, droplet impingement cooling and 3-D droplet movement driven by a thermocapillary force on a substrate with surface temperature gradients. (C) 2013 Elsevier Ltd. All rights reserved.