A triple phase-change lattice Boltzmann model, based on a coupling of existing vapor-liquid phase change model and enthalpy-based liquid-solid phase-change model, is proposed in this paper. Based on this novel model, 3D simulations for transient condensation of a dry saturated vapor and subsequent freezing at a circular cryogenic spot of an inclined hydrophobic surface are carried out. The dynamic morphologies of the droplet and ice are presented. Simulated results show that ice adjacent to the cryogenic spot is formed inside a droplet, and the droplet subsequently moves down along the vertical surface under action of gravity. Effects of droplet's dynamic behaviors on the growth of ice and averaged heat flux are presented. Temperature distributions in the ice as well as in the water and steam on the middle cross section and local heat flux at the wall are illustrated. Simulations of the triple phase-change phenomena under different tilt angles show that the ice is elongated in the direction of gravity. The wettability of the surface is shown to have important influence on the morphology of droplet but its effect on the growth of ice is small. (C) 2017 Elsevier Ltd. All rights reserved.