Ice slurry can be used as the thermal storage media in latent cool storage systems for both residential and commercial buildings. This paper presents the investigation of the phase change characteristics of the ice slurry using a two-fluid Lattice Boltzmann Method (TFLBM). The melting and migration processes of the ice slurry are simulated by improving the equilibrium distribution function and matching the relevant parameters such as the kinetic viscosity of ice particle cluster and cross-collision coefficient. The sensitivity analysis of the ice slurry viscosity and cross-collision coefficient are achieved through six numerical experiments, and the ice melting in the internal-melt ice-on-coil thermal storage device is then calculated. The results could be potentially used to guide the design of the ice slurry for cooling both residential and commercial buildings.