Clustering is an important technology of data mining, which plays a vital role in bioscience, social network and network analysis. As a clustering algorithm based on density and distance, density peak clustering is extensively used to solve practical problems. The algorithm assumes that the clustering center has a larger local density and is farther away from the higher density points. However, the density peak clustering algorithm is highly sensitive to density and distance and cannot accurately identify clusters in a dataset having significant differences in cluster structure. In addition, the density peak clustering algorithm's allocation strategy can easily cause attached allocation errors in data point allocation. To solve these problems, this study proposes a potential-field-diffusion-based density peak clustering. As compared to existing clustering algorithms, the advantages of the potential-field-diffusion-based density peak clustering algorithm is three-fold: 1) The potential field concept is introduced in the proposed algorithm, and a density measure based on the potential field's diffusion is proposed. The cluster center can be accurately selected using this measure. 2) The potential-field-diffusion-based density peak clustering algorithm defines the judgment conditions of similar points and adopts different allocation strategies for dissimilar points to avoid attached errors in data point allocation. 3) This study conducted many experiments on synthetic and real-world datasets. Results demonstrate that the proposed potential-field-diffusion-based density peak clustering algorithm achieves excellent clustering effect and is suitable for complex datasets of different sizes, dimensions, and shapes. Besides, the proposed potential-field-diffusion-based density peak clustering algorithm shows particularly excellent performance on variable density and nonconvex datasets.