A two-dimensional numerical simulation of Rayleigh-Benard convection in a rectangular enclosure heated from below and cooled from above has been conducted with non-Newtonian phase-change-material (PCM) microcapsulate slurries with latent heat capacities. The formulation of the mathematical model in dimensionless co-ordinates and discretization of the governing equations has been done using the finite volume method. Both flow and heat transfer characteristics are discussed about Rayleigh-Benard natural convection with PCM microcapsulate slurry, which exhibits pseudoplastic non-Newtonian fluid behavior and a peak value in the specific heat capacity. The viscosity of the present PCM microcapsulate slurry is assumed to follow the Ostwald-de Waele power law fluid model with the power-law index n and the consistency coefficient K. The effects of the mass concentration and the aspect ratio Ar on the natural convection are described respectively.