Considering the safety and effectiveness of lithium-ion batteries for new-energy vehicles under extreme working conditions, a topology optimization design method based on a bionic leaf-vein structure is proposed in this paper. Taking the liquid cooling plate for a lithium-ion battery as the research object, heat dissipation channels with a bionic leaf-vein structure were designed. The number, angle, width, and height of initial cold plate (ICP) were analyzed through orthogonal experiments. The optimized cooling plate (OCP) with a bionic leaf-vein structure was obtained by solving with the non-dominated sorting genetic algorithm-II (NSGA-II). Then, the two-dimensional structure of the OCP was used as the initial solution, and topology optimization was performed with an initially uniformly distributed density field. Maximum heat transfer and minimum dissipative work were used as the multi-objective functions to obtain the bionic topological cooling plate (BTCP) and the topological cooling plate (TCP). Finally, the performance of the BTCP and TCP were compared with that of the OCP. The results showed that the OCP has better heat dissipation compared to the ICP, with the maximum temperature (Tmax) reduced by 1.06 °C and maintained around 33 °C. Additionally, the pressure drop (ΔP) is reduced by 40.03%, and the standard temperature difference (Tσ) is reduced by 8.98%. The Tmax of the BTCP was reduced by 0.71 °C compared to that of the OCP. Furthermore, the ΔP and Tσ are reduced by 71.25% and 40.79%, respectively. Compared with the TCP, the thermal homogeneity of the BTCP increases by 29% even though the ΔP increases by 2.87 Pa. Analysis of the comprehensive indexes shows that the performance of the TCP and BTCP improves by 80% and 96%, respectively, on the basis of that of the OCP. Moreover, the BTCP features a better channel structure, which ensures thermal homogeneity and saves computation time of the model.