A single-relaxation-time (SRT) and a multiple-relaxation-time (MRT) thermal lattice Boltzmann models are developed for axisymmetric solid-liquid phase change. The axisymmetric enthalpy conservation equation can be recovered from these two models. Both the SRT and MRT models are verified by the finite volume method (FVM). Compared with the SRT model, the MRT one is superior on the numerical stability. The MRT model is also validated by the published experimental data and numerical results. The results suggest that the present models are qualified to simulate the axisymmetric solid-liquid phase change. Furthermore, the influence of the natural convection on the melting is also quantitatively discussed. How the Prandtl number affects the average Nusselt number along the hot wall and average liquid fraction is also explored. Results show that lower Prandtl number causes the flow in the liquid phase zone more unsteady. (C) 2017 Elsevier Ltd. All rights reserved.