Aiming at the problem that the clustering results of K-Means clustering algorithm are affected by the sample distribution because of using the mean to update the cluster centers， a Neural Tangent Kernel K-Means （NTKKM） clustering algorithm was proposed. Firstly， the data of the input space were mapped to the high-dimensional feature space through the Neural Tangent Kernel （NTK）， then the K-Means clustering was performed in the high-dimensional feature space， and the cluster centers were updated by taking into account the distance between clusters and within clusters at the same time. Finally， the clustering results were obtained. On the car and breast-tissue datasets， three evaluation indexes including accuracy， Adjusted Rand Index （ARI） and FM index of NTKKM clustering algorithm and comparison algorithms were counted. Experimental results show that the effect of clustering and the stability of NTKKM clustering algorithm are better than those of K-Means clustering algorithm and Gaussian kernel K?Means clustering algorithm. Compared with the traditional K?Means clustering algorithm， NTKKM clustering algorithm has the accuracy increased by 14.9% and 9.4% respectively， the ARI increased by 9.7% and 18.0% respectively， and the FM index increased by 12.0% and 12.0% respectively， indicating the excellent clustering performance of NTKKM clustering algorithm.