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Clustering is often seen as a more practical but very challenging answer to the task of categorizing objects. Minimum Sum-squared Residue for Fuzzy Co-Clustering (MSR-FCC) is proposed to address two issues faced by many existing clustering algorithms, namely the high-dimensionality and the inherent fuzziness found in most real-world data. MSR-FCC is able to simultaneously cluster data and features using fuzzy techniques. It suggests a new partitioning fuzzy co-clustering algorithm based on the mean squared residue approach. Besides handling overlap clusters, MSR-FCC offers the flexibility that allows the number of data clusters to be different from the number of feature clusters, which reflects the distribution characteristic inherited in real-world data. In this paper, mathematical formulation of MSR-FCC is derived and explained. Experiments were conducted on standard datasets to demonstrate that the proposed algorithm is able to cluster high-dimensional data with overlaps feasibly and at the same time, it provides a new and promising mechanism for improving the interpretability of the co-clusters through the fuzzy membership function.