As for multi-view datasets, direct integration of partition results of all views obtained by traditional single-view clustering approaches does not improve and even deteriorate the clustering performance since that it does not consider the inner relationship across views. To achieve good clustering performance for multi-view datasets, a multi-view clustering model is proposed, which not only considers the within-view clustering quality but also takes the cross-view collaborative learning into account. With respect to within-view partition, to capture more detailed information of cluster structures, a multi-medoid representative strategy is adopted; as for cross-view collaborative learning, it is assumed that a medoid of a cluster in one view is also a medoid of that cluster in another view. Based on the multi-view clustering model, a multi-view fuzzy clustering approach with a medoid invariant constraint (MFCMddI) is proposed in which the invariantan arbitrary medoid across each pair-wise views is guaranteed by maximizing the product of the corresponding prototype weightsin two views. The objective function of MFCMddI can be optimized by applying the Lagrangian multiplier method and KKT conditions. Extensive experiments on synthetic and real-life datasets show that MFCMddI outperforms the existing state-of-the-art multiview approaches in most cases.