In this paper, a lattice Boltzmann method for modelling and simulation of droplet dynamics on both chemically heterogeneous and microstructured partial wetting surfaces with large liquid–gas density ratio is developed and reported. Applying the method, the effects of surface chemistry and topography on motions of liquid drops are studied and analysed numerically. The obtained steady contact angles are in good agreement with those of theoretical prediction. Moreover, based on the evolutions of phase distribution and flow fields obtained from the numerical calculation, the corresponding mechanisms of droplet dynamics on partial wetting surfaces including droplet spreading, breaking up, migration as well as dynamic apparent contact angle, etc. are discussed and analysed.