The random and intermittent characteristics of distributed generations (DGs) of renewable energy will cause the point of common coupling (PCC) voltage of microgrid to fluctuate. Superconducting Magnetic Energy Storage (SMES) can be an effective approach to solve this problem. However, the operating current of SMES is often difficult to maintain stable, and for multiple paralleled SMESs, the difference in energy storage between SMESs will affect its ability to output/absorb power. In this paper, a renewable energy microgrid with SMESs based on current-source power conditioning system (PCS) is considered and its voltage stability of PCC is investigated. Aiming at the parallel connection of two SMESs, a double-layer fuzzy control strategy is proposed to manage the operating current of each SMES and realize the current sharing between two SMESs. The simulation results in MATLAB/Simulink demonstrate that the presented double-layer fuzzy control strategy can maintain the operating current of SMESs in the normal range, and realize the current sharing of two SMESs.