This article builds the fuzzy clustering algorithm for interval data (FCAI). In the pro- posed algorithm, we use the overlap distance as a criterion to cluster for interval data. The FCAI can determine not only the suitable number of clusters, the elements in each cluster but also the probability of assigning the elements to the established clusters at the same time. In addition, we also consider the convergence of the proposed algorithm by the theory and illustrated it by the numerical examples. The FCAI is applied well in image recognition, a problem with many challenges nowadays. Using the Grey Level Co-occurrence matrices (GLCMs), we propose a novel texture extraction approach to generate featured intervals. The complex computations of the FCAI can be performed conveniently and efficiently by the established Matlab program. We utilize the corrected rand indexes (CR) to find the suitable number of clusters while a partition entropy (PE) and partition coefficients (PC) are applied to argue the quality of fuzzy clusters. As a result, the experiments on the data sets having different characteristics and elements show the reasonableness of the proposed algorithm and its advantages in comparison to the existing ones. Regarding our best knowledge, it has also shown potential in the real application of this study.