Partially missing data sets are a prevailing problem in clustering analysis. In this paper, missing attributes are represented as intervals, and a novel fuzzy c-means algorithm for incomplete data based on nearest-neighbor intervals is proposed. The algorithm estimates the nearest-neighbor interval representation of missing attributes by using the attribute distribution information of the data sets sufficiently, which can enhances the robustness of missing attribute imputation compared with other numerical imputation methods. Also, the convex hyper-polyhedrons formed by interval prototypes can present the uncertainty of missing attributes, and simultaneously reflect the shape of the clusters to some degree, which is helpful in enhancing the robustness of clustering analysis. Comparisons and analysis of the experimental results for several UCI data sets demonstrate the capability of the proposed algorithm.