Maximal biclique enumeration is a fundamental research problem in the bipartite graph analysis field. However, the traditional biclique model, which requires the subgraph to be a complete bipartite graph, is often overly constrained in practical applications, and thus some looser biclique models are needed to substitute. In this study, a new relaxation biclique model called k-defective biclique is proposed. This model allows a bipartite subgraph to differ from a complete bipartite subgraph biclique by up to k edges. Since enumerating maximal k-defective bicliques is NP-hard, designing efficient enumeration algorithms is a challenging task. To solve this problem, an algorithm based on symmetric set enumeration is proposed. The idea of this algorithm is to control the number of sub-branches through a constraint on the number of missing edges in the k-defective bicliques. To further improve the computational efficiency, a series of optimization techniques are also proposed, including ordering-based subgraph partitioning method, upper-bound based pruning method, linear time-based updating technique, and optimization method for branching. In addition, the time complexity of the proposed optimization algorithms is related to, where breaks through the traditional limitation. Finally, a large number of experimental results show that the efficiency of the proposed method is over a hundred times higher than that of the traditional branch-and-bound approach for most parameter settings.