Concentrator photovoltaics is a promising technique for enhancing the utilisation of solar energy while decreasing the system cost. Employing the concentrator photovoltaics allows the replacement of expensive solar cell area with lower-in-cost lenses or mirrors. However, concentrating the solar radiation on solar cell leads to a dramatic rise in its temperature, and reduction in its efficiency and lifetime. Passive cooling is considered in this work as it is noiseless, and no maintenance or power is required to keep it working. The effect of attaching fins along with phase change material (PCM) to the back of the solar cell under concentrated radiation on the thermal management of concentrator photovoltaics is numerically investigated. In addition, uncooled concentrator photovoltaics, concentrator photovoltaics integrated with metal sheet heat spreader and Concentrator photovoltaics attached to horizontal fins are examined with the aim of comparing with fins filled with PCM case. The solar cell temperature, as well as liquid fraction of phase change material, are the key judging parameters. The results show that adding the PCM to fins can effectively enhance the thermal regulation of the concentrator photovoltaics compared to other methods, permitting a further increase of the concentration ratio and allowing for waste heat recovery from the system. However, the phase change material thermal regulation time is limited and determined by the amount of phase change material used as the wax is acting as a thermal insulator after it fully melts.