The unbalanced state of charge (SOC) of distributed energy storage systems (DESSs) in autonomous DC microgrid causes energy storage units (ESUs) to terminate operation due to overcharge or overdischarge, which severely affects the power quality. In this paper, a fuzzy droop control for SOC balance and stability analysis of DC microgrid with DESSs is proposed to achieve SOC balance in ESUs while maintaining a stable DC bus voltage. First, the charge and discharge modes of ESUs are determined based on the power supply requirements of the DC microgrid. One-dimensional fuzzy logic is then applied to establish the relationship between SOC and the droop coefficient R_d in the aforementioned two modes. In addition, when integrated with voltage-current double closed-loop control, SOC balance in different ESUs is realized. To improve the balance speed and precision, an exponential acceleration factor is added to the input variable of the fuzzy controller. Finally, based on the average model of converter, the system-level stability of microgrid is analyzed. MATLAB/Simulink simulation results verify the effectiveness and rationality of the proposed method.