Medium and high-temperature latent heat thermal energy storage (LHTES) systems with high energy density can manage the intermittency of renewable energy sources. However, some significant challenges remain to be addressed. Hence, in this article, a pilot-scale medium-temperature cylindrical LHTES system loaded with 4130 kg phase change material (PCM) and equipped with heat exchanger tubes featuring spiral and H-shaped fins was constructed. The temperature evolution of PCM and various parameters containing charging/discharging time, instantaneous power, accumulated energy, and efficiency under the constant temperature and the step temperatures methods were investigated. The experimental results revealed that the melting of the upper PCM was accelerated by natural convection, whereas the melting of the bottom PCM was slower due to heat conduction. The heat exchange tubes with spiral fins demonstrated better performance during the charging process, whereas those with H-shaped fins performed better during the discharging process. In addition, the LHTES system achieved accumulative energy storage of 993.64 MJ and release of 659.58 MJ with a cycle efficiency of 66.38% under the constant temperature method. However, the accumulative energy storage and release under the step temperatures method were 966.2 and 664.86 MJ, respectively, with a cycle efficiency of 68.81%.