Proper design of the cooling plate is crucial for ensuring the safety and stability of a battery module. In this paper, we propose a topology optimization approach based on the density model to design the topological cooling channel. To meet different cooling and power consumption requirements, we propose a multi-objective function that weighs the cooling performance and pump power consumption. We couple the heat transfer model of the cooling plate with an electrochemical multiphysics model that can simulate the constant voltage charging process of NMC111 ternary material lithium battery. We comprehensively analyze the effects of different weight factors, Reynolds number, and heat coefficient on the flow and temperature distributions. Our results show that increasing the Reynolds number improves fluid velocity and cooling performance, while increasing the heat coefficient can lead to the occurrence of a heat concentration area. In addition, a larger weight factor can decrease the temperature of the battery pack but increase the pressure drop of the cooling plate. Finally, we obtain the Pareto front of the cooling plate design to meet different engineering needs.