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Road traffic accidents occur frequently and seriously in the accident-prone spots. In order to improve the safety and efficiency of road traffic, it is necessary to find the location of accident-prone points. The existing density clustering algorithm needed to set the number of center points and was easy to expand the clustering range when identifying traffic accident-prone points, this paper proposed the limit cluster expansion and adaptive search clustering by fast search and find of density peaks (LA-CFDP) algorithm to solve these problems. LA-CFDP algorithm automatically determined the number of center points by increasing the restriction condition of center points, and introduced the parameter expansion factor to limit the cluster expansion range, so as to improve the adaptability and accuracy of the algorithm for accident-prone point identification. The case analysis on the 2019 traffic accident data set of four cities in United Kingdom shows that the Sihouette coefficient of the clustering results of LA-CFDP algorithm reaches 0.72～0.92, and the Davies-Bouldin index (DBI) are all reduced to below 0.37. The clustering results accord with the definition and characteristics of accident-prone spots, and can provide reliable basis for the management of accident-prone spots. [ABSTRACT FROM AUTHOR]