A comprehensive study of the melting process inside a capsule can potentially take full advantages of latent heat of phase change materials (PCMs). The present study was devoted to the problem of complex interaction of natural convection and melting of PCMs inside a spherical capsule under different sizes. The numerical results, simulated by lattice Boltzmann method (LBM), were compared with experimental data and published simulations. The results showed that LBM presented desirable accuracy compared to traditional computational fluid dynamics (CFD) methods. Then, the effects of non-uniform PCM properties, expressed by the solid/liquid thermal diffusivity ratio, on the melting rate were found to be nonlinear in different melting stages. The non-dimensional fully melting time reduced with the increase of the surface temperature and the capsule size, and the former compared to the latter could have a greater influence on the melting rate. Moreover, the non-dimensional fully melting time reduced when increasing of the capsule diameter at the macro-scale; while there was a near-invariable non-dimensional fully melting time when the capsule size was changed at the micro-scale. The good understanding of the phase change process inside the capsule would provide essential information to develop a multi-scale model of microencapsulated PCM slurries. (C) 2018 Elsevier Ltd. All rights reserved.