Since data are collected from a range of sources via different techniques, multiview clustering has become an emerging technique for unsupervised data classification. However, most existing soft multiview clustering methods only consider the pairwise correlations and ignore high-order correlations among multiple views. To integrate more comprehensive information from different views, this article innovates a fuzzy clustering model using the low-rank tensor to address the multiview data clustering problem. Our method first conducts a standard fuzzy clustering on different views of the data separately. Then, the obtained soft partition results are aggregated as the new data to be handled by a Kullback-Leibler (KL) divergence-based fuzzy model with low-rank tensor constraints. The KL divergence function, which replaces the traditional minimized Euclidean distance, can enhance the robustness of the model. More importantly, we formulate fuzzy partition matrices of different views as a third-order tensor. So, a low-rank tensor is introduced as a norm constraint in the KL divergence-based fuzzy clustering to obtain dexterously high-order correlations of different views. The minimization of the final model is convex and we present an efficient augmented Lagrangian alternating direction method to handle this problem. Specially, the global membership is derived by using tensor factorization. The efficiency and superiority of the proposed approach are demonstrated by the comparison with state-of-the-art multiview clustering algorithms on many multiple-view data sets.