Uncertainties included in soft classification exist in classical mathematics. However, in daily life, the extended fuzzy concept has much information, and the clustering algorithm established on fuzzy set for fuzzy samples has been poorly investigated. To solve above problems, this study made improvements on DBSCAN and proposed a DBSCAN algorithm based on fuzzy numbers. Using this algorithm, classical information included in the samples is extended to fuzzy sets, and fuzzy samples can be clustered by searching the density peak. In other words, this algorithm is a kind of fuzzy clustering algorithm on the basis of fuzzy set. Firstly, the related concepts of fuzzy number were briefly introduced; then, by means of error analysis, improved Euclidean distance between fuzzy numbers was defined based on the definition of traditional Euclidean distance, and some key parameters or operating quantities mainly including cut-off distance and Gaussian Kernal function of fuzzy samples were introduced in detail. By referring to the procedures of DBSCAN, the detailed procedures using algorithm were described. Next, we applied this algorithm to Personal Credit Reference System, compared with other hierarchical clustering algorithms; it can be found that this algorithm has better results. Finally, both advantages and disadvantages of the proposed algorithm were concluded and some recommendations for improvement were put forward, which can provide insightful guidance for further investigations of fuzzy clustering algorithms on fuzzy sets.