The performance of a new type of latent heat thermal energy storage (LHTS) device based on flat micro-heat pipe arrays (FMHPAs) with longitudinal rectangular fins is numerically studied by enthalpy-porosity technique based on finite volume method (FVM) in this research. The numerical model is verified correct. The temperature distribution and phase transition process in different directions of the interior of a thermal storage tank and the effects of fin height, spacing, and thickness on charging power and thermal storage capacity are also analyzed numerically. Results show that phase interface is presented in U type in the horizontal direction. In the vertical direction, the phase change material (PCM) among fins melts from up to down when the fin spacing is larger than 6 mm, and the opposite occurs when the fin spacing is less than 6 mm. The thermal storage capacity of the LHTS device is reduced drastically when the fin spacing is less than 4.14 mm. For fin height, the structure of multiple rows of FMHPAs with dwarf fins is recommended because it exhibits large power and exerts a small negative effect on thermal storage capacity. Fin thickness has a minimal effect on charging power and thermal storage capacity. The study results provide optimization design guidance for LHTS devices based on FMHPAs under various application backgrounds, such as solving the contradiction between energy supply and demand in solar thermal systems and the peak load shifting of electricity in heat pump systems.