For a latent heat thermal energy storage (LHTES) unit, its heat transfer performance can be significantly enhanced by increasing the fin surface. The LHTES unit with an annular heat source (AHS) is proposed for different shape fins and structural parameters. A corresponding numerical simulation has been conducted. The results show that pipe diameter ratio gamma has the greatest influence on the heat transfer power Phi, followed by the outer and inner fin type in the charging and discharging processes. The increase of gamma from 0.55 to 0.7 leads to tc decreasing by 62.65%, the charging power Phi c increasing by 153.68%, and the wall-average Nusselt number Nuc in the charging process increasing by 45.47%. Furthermore, an optimal gamma of 0.625 is identified for the discharging process, resulting in -29.61%, 38.27%, and 20.2% changes in td, the discharging power Phi d, and the wall-average Nusselt number Nud in the discharging process compared to gamma of 0.55. Bifurcation angle theta significantly influences tc and td. The optimal theta for the charging process is 60 degrees, reducing tc by 40.7% compared to that of 180 degrees. For the discharging process, the optimal theta is 90 degrees, reducing td by 8.81%. The number of branches n significantly impacts heat transfer by influencing heat conduction. For the charging process, increasing n from 4 to 14 results in -45.39%, 81.78%, and -39.67% changes in tc, Phi c, and Nuc, respectively, while during the discharging process, it leads to changes of -31.91%, 45.48%, and -25.91% in td, Phi d, and Nud, respectively.