Enumerating minimal unsatisfiable subsets (MUS) is an important subproblem in the Boolean satisfiability problem. For an unsatisfiable problem, the MUS enumeration can reflect the key factors resulting in its unsatisfiability. However, enumerating MUS is extremely time-consuming, and different pruning schemes will directly affect the size of the search space and the total number of iterations, thus affecting the algorithm efficiency. This study proposes a novel enhanced pruning scheme, accelerating by critical MSS (ABC), to accelerate the MUS enumeration. According to the relationship among maximal satisfiable subsets (MSS), minimal correction sets (MCS), and MUS, the concepts of cMSS and subMUS are put forward. Additionally, four properties are summarized, namely that each MUS must be a superset of subMUS, and then the feature that MUS and MCS are mutually hitting sets can be effectively employed to avoid the time cost in solving hitting sets of MCS. When the subMUS is unsatisfiable, it will be the only MUS, and the algorithm will terminate in advance; otherwise, the node representing subMUS will be pruned to effectively avoid searching the non-solution space. Meanwhile, the effectiveness of the proposed ABC scheme is proven by theorem, which has been applied to the state-of-the-art algorithms MARCO and MARCO-MAM, respectively. Experimental results on SAT11 MUS benchmarks show the proposed scheme can effectively prune the search space to improve the enumeration efficiency of MUS.