It has been shown that most traditional clustering algorithms for categorical data that only optimize a single criteria suffer from some limitations, thus a novel multiobjective fuzzy clustering is proposed, which simultaneously considers within-cluster and between-cluster information. The lately reported algorithms are all based on K-modes, and the more accurate algorithm fuzzy centroids is utilized as the base algorithm to design the proposed method. Fuzzy membership is used as chromosome that is different from traditional genetic based hybrid algorithms, and a set of optimal clustering solutions can be produced by optimizing two conflicting objectives simultaneously. Meanwhile, a termination criterion in advance which can reduce unnecessary computing cost is used to judge whether the algorithm is steady or not. To further improve the efficiency of the proposed method, fuzzy centroids can be calculated using a subset of the dataset, and then the membership matrix can be calculated by these centroids to obtain the final clustering result. The experimental results of 10 datasets show that the clustering accuracy and stability of the proposed algorithm is better than the state of art multiobjective algorithm, and also the computing efficiency is improved to a large extern.