Basing on L1-distance and representing element of cluster, the article proposes new three algorithms in Fuzzy Clustering of probability density Functions (FCF). They are hierarchical approach, nonhierarchical approach and the algorithm to determine the optimal number of clusters and the initial partition matrix to improve the qualities of established clusters in non-hierarchical approach. With proposed algorithms, FCF has more advantageous than Non-fuzzy Clustering of probability density Functions. These algorithms are applied for recognizing images from Texture and Corel database and practical problem about studying and training marks of students at an university. Many Matlab programs are established for computation in proposed algorithms. These programs are not only used to compute effectively the numerical examples of this article but also to be applied for many different realistic problems.