The charging enhancement of latent heat thermal energy storage system is of great significance for the efficient transfer of non-uniform thermal sources. In order to solve the problem of long charging time caused by the low thermal conductivity of phase change materials (PCMs), multiple PCMs - uneven fins combination as a compound enhancement approach was proposed to improve thermal storage rate. The transient heat transfer and melting process of PCMs was numerically studied by the finite volume method and enthalpy-porosity method. Firstly, the filling ratio of high melting point PCM to high melting point PCM was optimized as 60%: 40%. Under the optimal ratio, the charging time was reduced by 29% and the thermal storage rate was increased by 9%. Then, the effect of natural convection on multiple PCMs melting characteristics was analyzed. Finally, the thermal storage performance of multiple PCMs - uneven fins combination was investigated. The results indicated that the reasonable fin arrangement (upper dense - lower sparse fins) strengthens the local convection and improves the melting uniformity, which reduces the melting time by 16% and increases the thermal storage rate by 7%. Therefore, multiple PCMs - uneven fins combination can obviously reduce the charging time and increase the thermal storage capacity, which contributes to promote efficient utilization of fluctuating thermal energy.