Latent heat storage has advantages of high energy storage density, safety, and high efficiency, which thereby has broad application prospects in the field of industrial waste heat recovery. However, the low thermal conductivity of phase change materials (PCMs) has become the main problem that restricts the application of latent heat thermal energy storage (LHTES) system. In this paper, an innovative circular superimposed longitudinal fin was proposed to enhance the heat transfer performance of LHTES system. Ternary eutectic salt of Li2CO3-K2CO3-Na2CO3 (32–35–33wt%) was selected as the PCM. The heat release performance and exergy efficiency of shell-and-tube LHTES unit with the innovative fins were studied by numerical simulation with the use of solidification and melting model in ANSYS FLUENT V16.0. The results showed that circular superimposed longitudinal fins significantly improved the solidification performance of PCM in LHTES unit. Compared with the traditional rectangular fin (Fin-A), circular superimposed fins with ever-decreasing arrangement (Fin-C) were found to have the best heat transfer performance, and the solidification time of PCM was shortened by 38.72%. Furthermore, the exergy analysis of LHTES unit with Fin-C during heat release process was performed. The specific exergy of HTF decreased rapidly at the beginning over time and then tended to slow down when phase change process occurred on PCMs. However, the turning point was delayed and the gradient after the turning point decreased with the increase of the temperature, which was not affected by the inlet velocity. The heat extraction exergy efficiency of LHTES unit increased linearly with the increase of inlet temperature and decreased nonlinearly with the increase of inlet velocity. Meanwhile, the heat release exergy efficiency of LHTES unit reduced linearly with the increase of inlet temperature, but was almost not affected by the inlet velocity. In order to ensure that the heat extraction exergy efficiency is higher than 95%, and taking into account the higher heat release exergy efficiency, it is recommended to set the inlet temperature and velocity at 607 K and 1.8 m/s, respectively.