By extending CFSFDP algorithm to continuous fuzzy sets and discrete fuzzy sets, an extended CFSFDP algorithm for fuzzy mixed data is proposed, which is named FMD-CFSFDP algorithm. The FMD-CFSFDP algorithm extends the classical information in the sample to fuzzy sets, and achieves the clustering of fuzzy sets by seeking the density peaks. The proposed FMD-CFSFDP algorithm is a kind of density-based clustering algorithm established on fuzzy set for fuzzy mixed data. Firstly, the CFSFDP algorithm and some of its improvement algorithms are briefly introduced, and the mathematical definition of fuzzy mixed data is given. Secondly, by combining the concept of traditional fuzzy Euclidean distance, the improved Euclidean distance for both continuous and discrete fuzzy sets with smaller error is proposed. On the basis, the weight is introduced to establish the overall distance for fuzzy mixed data. By referring to the clustering steps of the CFSFDP algorithm, the clustering steps of FMD-CFSFDP algorithm are given. Furthermore, under the conditions of different sample size, different index number, different cluster number and different fetching rule, random simulation experiments are carried out on the algorithm and the clustering results are analyzed. Finally, the advantages and disadvantages of the FMD-CFSFDP algorithm are summarized respectively. On this basis, some improved schemes are proposed, which provides a reference for future in-depth research.