Random walks are a standard tool for modeling the spreading process in social and biological systems. But in the face of large-scale networks, to achieve convergence, iterative calculation of the transition matrix in random walk methods consumes a lot of time. In this paper, we propose a three-stage hierarchical community detection algorithm based on Partial Matrix Approximation Convergence (PMAC) using random walks. First, this algorithm identifies the initial core nodes in a network by classical measurement and then utilizes the error function of the partial transition matrix convergence of the core nodes to determine the number of random walks steps. As such, the PMAC of the core nodes replaces the final convergence of all the nodes in the whole matrix. Finally, based on the approximation convergence transition matrix, we cluster the communities around core nodes and use a closeness index to merge two communities. By recursively repeating the process, a dendrogram of the communities is eventually constructed. We validated the performance of the PMAC by comparing its results with those of two representative methods for three real-world networks with different scales.