Latent heat storage (LHS) has found extensive applications across various fields. However, large-scale deployment is still restricted due to the worse thermal charging performance of traditional LHS systems. In this research, the self-growing fins of the tube-shell LHS system are designed via the bionic topology optimized method to improve thermal storage performances, inspired by the structures and functions of leaf veins. Notably, the system installed with topology-optimized self-growing fins (T-FIN) demonstrates the shortest melting time, largest specific power density (SPD), and highest efficiency simultaneously. At the inlet conditions of 0.5 L·min-1 and 358.15 K, the thermal charging time decreases by 46.4% and 57.1% compared with the systems equipped with traditional long-fins (L-FIN) and short-fins (S-FIN), while increasing the SPD by 80.6% and 125.7%, respectively. Moreover, the efficiency of exergy and entransy storage is 2.49 and 2.42 times, respectively, as large as those of the S-FIN. The intrinsic mechanism is attributed to enhanced synergy between the liquid-PCM temperature field and the flow field. Furthermore, outer tube shapes are optimized by the Genetic Algorithm for the first time, leading to a further decrease in charging time by 21.57% compared with its original counterpart. These findings provide a valuable idea for designing efficient bionic LHS systems.