Density peaks clustering (DPC) is a density-based clustering algorithm that can intuitively determine the number of clusters, identify clusters of any shape, and automatically detect and exclude abnormal points. However, DPC still has some shortcomings: The DPC algorithm only considers the global distribution, and the clustering performance is poor for datasets with large cluster density differences. In addition, the point allocation strategy of DPC is likely to cause a domino effect. Hence, this study proposes a DPC algorithm based on representative points and K-nearest neighbors (KNN), namely, RKNN-DPC. First, the KNN density is constructed, and the representative points are introduced to describe the global distribution of samples and propose a new local density. Then, the KNN information of samples is used to propose a weighted KNN allocation strategy to relieve the domino effect. Finally, a comparative experiment is conducted with five clustering algorithms on artificial datasets and real datasets. The experimental results show that the RKNN-DPC algorithm can more accurately identify cluster centers and obtain better clustering results.