Latent heat thermal energy storage systems hold great potential for efficient thermal energy storage, but their development is limited by the low thermal conductivity of storage materials. In this study, we propose a bionic topology structure based on three evenly distributed inner tubes for application in a horizontal latent heat storage device. Utilizing the Taguchi design method, we first identified the optimal arrangement of the inner tubes, achieving an eccentricity of 0.7 and a tube rotation angle of 0 degrees. Building on this arrangement, we designed topology-optimized fins and established the optimal range for the fin volume fraction, taking into account energy storage density, heat storage and release rates, and economic costs. Subsequently, we considered the influence of natural convection on phase change heat transfer and compared four different heat storage models, including those with topology-optimized fins, analyzing their heat transfer and flow characteristics during the melting and solidification processes. The findings indicated that the three-tube arrangement optimized through the Taguchi design reduced the single-cycle heat storage and release time by 53.49% while increasing the heat cycle rate by 2.22 times. Furthermore, incorporating a topology structure into the three-tube arrangement enhanced the heat cycle rate by an additional 2.08 times compared to traditional fin structures, while the temperature distribution non-uniformity of the phase change material during melting and solidification decreased by 65.32% and 85.26%, respectively. Additionally, we observed that the topology-optimized fin structure exhibits fractal dimensions akin to those found in natural forms, such as leaf veins and snowflakes. This study offers a novel approach for the performance optimization of latent heat storage systems.