The performance of a thermal energy storage (TES) system for commercial applications can be improved using phase change materials (PCM). This study develops a vertical multi-module from a PCM for a TES system that achieves the same effect as a single-module by arranging multiple-modules in series as a U-type longitudinal fin tube to enhance the system's performance. The U-type longitudinal fin tube is designed to enhance heat transfer within the module, and a single-module is designed for multi-module applications. The TES system is analyzed to the average heat transfer rate, overall heat transfer coefficient, quantity of heat storage/release, and utilization ratio at different heat transfer fluid (HTF) flow rates, inlet and outlet temperatures and different number of modules. Consequently, the addition of several modules improves the thermal performance, and an increase in the HTF flow rate improves the average heat transfer rate. The overall heat transfer coefficient is used to analyze the thermal characteristics of the PCM. During the heat charging and discharging processes, the average heat transfer rates are 2.4 and 2.55 kW, respectively, and the quantities of heat storage and release are 5,153.59 and 4,771.79 kJ, respectively, for three modules. The overall heat transfer coefficient of the PCM exhibits similar results with an increasing HTF flow rate; it increases marginally from 42.25 to 45.8 and 9.9–10.8 W∙m−2∙K−1 as more modules are added. Further, the results of this study confirm that the relatively low HTF flow rates in the multi-module require the addition of several modules and that increasing the HTF flow rates limits the number of modules.