A fin enhanced cooling of a Solar Concentrated Photovoltaic Thermal (CPV-T) receiver is studied with the new computational method, i.e., an improved Lattice Boltzmann Method (LBM). Transient flow patterns and temperature fields have been obtained by the mesoscopic scale simulations with Non-dimensional Lattice Boltzmann Methods (NDLBM). The results show that the application of metal fins such as material copper will enhance the cooling slightly, while glass fins are not friendly to enhance heat transfer although they can keep high light transportation ratio. Geometry factors such as fin heights, gap distance, and thicknesses are also compared. It is found out that shorter smaller gap thicker fins are better designs because they reduce the impeding effects on fluid flow and increase the heat transfer areas between solid and fluid phases.