K-means algorithm is a widely used clustering algorithm, but the selection of the initial clustering centers in the traditional K-means algorithm is random, which makes the algorithm easily fall into local optimum and causes instability in the clustering result. In order to solve this problem, the idea of multi-dimensional grid space was introduced to the selection of initial clustering center. Firstly, the sample set was mapped to a virtual multi-dimensional grid space structure. Secondly, the sub-grids containing the largest number of samples and being far away from each other were searched as the initial cluster center grids in the space structure. Finally, the mean points of the samples in the initial cluster center grids were calculated as the initial clustering centers. The initial clustering centers chosen by this method are very close to the actual clustering centers, so that the final clustering result can be obtained stably and efficiently. By using computer simulation data set and UCI machine learning data sets to test, both the iterative number and error rate of the improved algorithm are stable, and smaller than the average of the traditional K-means algorithm. The improved algorithm can effectively avoid falling into local optimum and guarantee the stability of clustering result.