A model of vapor condensation on a solid surface is developed and numerically analyzed using the free energy lattice Boltzmann method. Based on the model, the condensation phase change on hydrophobic, hydrophilic and gradient surfaces are simulated with a particular focus on the condensation on a gradient surface. The droplet nucleation, growth, deformation, coalescence and motion during the condensation on a gradient surface are investigated. The present simulation reproduces the self-propelled dropwise condensation on a gradient surface, the film condensation on a hydrophilic surface and the conventional dropwise condensation on a hydrophobic surface. The results indicate that the condensed droplets on a gradient surface can be swept in time to provide a favorable condition for the subsequent condensation. On a smooth gradient surface, owing to the unbalanced wetting force, the vapor condenses into a thin film firstly and then fractures into droplet nucleation as the condensation process goes on. The larger wettability gradient results in a larger amplitude oscillation of condensation rate and a slighter variation of surface coverage. (C) 2017 Elsevier Ltd. All rights reserved.