Spike sorting is used to classify the spikes (action potentials acquired by physiological electrodes), aiming to identify their respective firing units. Now it has been developed to classify the spikes recorded by multi-electrode arrays (MEAs), with the improvement of micro-electrode technology. However, how to improve classification accuracy and maintain low time complexity simultaneously becomes a difficulty. A fast and accurate spike sorting approach named HTsort is proposed for high-density multi-electrode arrays in this paper. Several improvements have been introduced to the traditional pipeline that is composed of threshold detection and clustering method. First, the divide-and-conquer method is employed to utilize electrode spatial information to achieve pre-clustering. Second, the clustering method HDBSCAN (hierarchical density-based spatial clustering of applications with noise) is used to classify spikes and detect overlapping events (multiple spikes firing simultaneously). Third, the template merging method is used to merge redundant exported templates according to the template similarity and the spatial distribution of electrodes. Finally, the template matching method is used to resolve overlapping events. Our approach is validated on simulation data constructed by ourselves and publicly available data and compared to other state-of-the-art spike sorters. We found that the proposed HTsort has a more favorable trade-off between accuracy and time consumption. Compared with MountainSort and SpykingCircus, the time consumption is reduced by at least 40% when the number of electrodes is 64 and below. Compared with HerdingSpikes, the classification accuracy can typically improve by more than 10%. Meanwhile, HTsort exhibits stronger robustness against background noise than other sorters. Our more sophisticated spike sorter would facilitate neurophysiologists to complete spike sorting more quickly and accurately.