Repetitive pulsed high magnetic field (RPHMF) provides a novel solution for the frontier researches in the areas of condensed matter physics, materials science, biomedicine, and so on. Significant amount of attentions have been paid to the study of RPHMF by researchers. As the higher demand for magnetic field intensity and pulse frequency of RPHMF, the repeated supplement of energy storage and the thermal design of the magnet are enormous challenging at the same time. In the traditional design methods, the magnet and the power supply are designed step by step. However, the design of the power supply and the magnet is constrained by various factors including stress，power, current, voltage and temperature rise. Besides, these factors may interact and restrict each other. Therefore, it is hard to meet the design requirements of nonlinear complex systems with high power and strong coupling by traditional design methods. Based on the nonlinear dynamic analysis of the power supply and magnet, a mathematical model is built for the collaborative optimization in this paper. Accordingly a multi-objective design method of iterative algorithm for the overall optimization of the power supply and the magnet is proposed, which is combined by pareto-based differential evolution algorithm，real-time digital simulation, structure design of magnet and finite element analysis.In this paper, a 5T 20Hz RPHMF is designed by this multi-objective optimization algorithm for relativistic backward wave oscillator(RBWO)，which is used to generate high power microwave. Simulation and experiments results show that overall optimization of the magnet temperature rise, magnetic field intensity and continuous working times is realized. Therefore this multi-objective collaborative optimization design is feasible and this design method is of great application for RPHMF.