In this study, a new fuzzy co-clusterins algorithm based on a q-multinomial mixture model is proposed. A conventional fuzzy co-clustering model was constructed by fuzzifying a multinomial mixture model (MMM) via regularizing Kullback-Leibler divergence appearing in a pseudo likelihood of an MMM. Furthermore, a q-multinomial distribution was formulated, which acts as the Tsallis statistical counter for multinomial distributions in standard statistics. The proposed algorithm is constructed by fuzzifying a q-multinomial mixture model, by means of regularizing q-divergence appearing in a pseudo likelihood of the model. The proposed algorithm not only reduces into the q-multinomial mixture model, but also reduces into conventional fuzzy co-clustering models with specified sets of parameter values. In numerical experiments, the properties of the membership of the proposed method are observed.