Aiming at the problems of long equalization time and large energy loss in the equalization process of series-connected lithium-ion battery packs, a two-level equalization topology is designed in this paper, and a variable universe fuzzy Logic control strategy based on battery state of charge is designed for this topology. The proposed topology adopts an improved Buck-Boost circuit within the battery pack to optimize the equalization path, and a centralized single-inductance equalization circuit is used between the battery packs, which can achieve equalization between any battery packs. The proposed strategy introduces a contraction-expansion factor on the basis of fuzzy logic control to flexibly regulate the input domain, which further improves the equalization speed and energy utilization by precisely adjusting the equalization current. Finally, the equalization system is built for validation, and the results show that the topology of this paper reduces the equalization time by about 12.53% compared to the grouped Buck-Boost topology. Under the same static and charging/discharging conditions, the strategy in this paper not only reduces the equalization time by about 20.98% but also improves the energy utilization by about 7% compared with the FLC algorithm. The feasibility of the equalization scheme in this paper is verified.