A density peaks clustering(DPC) algorithm is efficient and effective in identifying clusters of arbitrary shapes. However, it has difficulty accurately determining cluster centers in datasets with significant inter-cluster density variations. Additionally, its assignment strategy may lead to consecutive allocation errors. To address these issues, we propose a k-nearest neighbor graph-based density peaks clustering(kNNG-DPC) algorithm. Firstly, both global and local k-nearest neighbor graphs are constructed using the k-nearest neighbor method. Based on these graphs, the algorithm introduces novel measures of local density and relative path distance, ensuring accurate cluster center selection. Furthermore, a two-stage allocation strategy is applied, employing different assignment methods for data points based on their density levels, effectively preventing consecutive allocation errors. The kNNG-DPC algorithm is evaluated against 6 advanced clustering algorithms on 10 synthetic datasets and 8 real-world datasets. Experimental results show that the clustering performance of the kNNG-DPC algorithm outperforms the benchmark algorithms, achieving superior clustering performance.