In this paper, a new robust fuzzy clustering approach is proposed for better performing principal component analysis (PCA) on function curves and character images that not only have loops, sharp corners, and intersections but also are bound of noise and outlier data. The proposed method is composed of two phases: firstly, input data are clustered using the proposed distance analysis to get good initial cluster centers and a reasonable number of clusters; secondly, the input data are further reclustered by the proposed robust fuzzy c-means (RFCM) based on the results obtained in the first phase to overcome the influence of noise and outlier data so that a good result of principal components can be found. Several function curves and Chinese character images are given to illustrate the effectiveness of the proposed method. Experimental results have demonstrated that the proposed approach works very well on PCA for both curves and images despite the fact that their input data sets may include loops, corners, intersections, noise, and outlier information.