Clustering algorithm based on the minimum spanning tree (MST) can identify clusters with arbitrary shapes, but the algorithm has limitations in efficiently constructing a minimum spanning tree and identifying invalid edges and is easily influenced by noise points. This study proposes an MST clustering algorithm based on local density peaks and label propagation (DPMST) by combining the advantages of the density peaks clustering algorithm to find local density peaks and exclude noise points with the MST algorithm. The DPMST algorithm adopts the shared neighbors-based distance between local density peaks and uses the neighborhood information between local density peaks to efficiently construct minimum spanning trees and identify invalid edges, enabling the discovery of clusters with complex structures. Label propagation is used to enhance the strong labels and weaken the weak labels to refine wrong labels, which can improve the quality of clustering results, especially for border region points as well as revealing complex manifolds. The experimental results on several synthetic and real-world datasets show that the DPMST algorithm outperforms classical clustering algorithms DPC, MST, K-means, DBSCAN, AP, SC, and BIRCH.