Since most existing single-prototype clustering algorithms are unsuitable for complex-shaped clusters, many multi-prototype clustering algorithms have been proposed. Nevertheless, the automatic estimation of the number of clusters and the detection of complex shapes are still challenging, and to solve such problems usually relies on user-specified parameters and may be prohibitively time-consuming. Herein, a stable-membership-based auto-tuning multi-peak clustering algorithm (SMMP) is proposed, which can achieve fast, automatic, and effective multi-prototype clustering without iteration. A dynamic association-transfer method is designed to learn the representativeness of points to sub-cluster centers during the generation of sub-clusters by applying the density peak clustering technique. According to the learned representativeness, a border-link-based connectivity measure is used to achieve high-fidelity similarity evaluation of sub-clusters. Meanwhile, based on the assumption that a reasonable clustering should have a relatively stable membership state upon the change of clustering thresholds, SMMP can automatically identify the number of sub-clusters and clusters, respectively. Also, SMMP is designed for large datasets. Experimental results on both synthetic and real datasets demonstrated the effectiveness of SMMP.