A novel nonlinear control strategy, the dynamic evolution control (DEC), is proposed for superconducting magnetic energy storage (SMES) converter under unbalanced power grid voltage conditions. Compared with traditional PI control, this control method can effectively reduce the three-phase current distortion and the second harmonic generated by active and reactive power caused by voltage unbalance of SMES. Firstly, three objectives are set according to the working conditions of SMES converter under the unbalanced power grid; secondly, the unbalanced control equation based on DEC is established, and the model is built in Simulink for simulation analysis. Finally, compared with the traditional PI control, DEC control has stronger robustness and faster response ability, the theoretical analysis and simulation results verify the feasibility and effectiveness of the control strategy.