In the classical k-means algorithm, the value of k must be confirmed in advance. It is difficult to confirm accurately the value of k in reality. This paper proposes an improved genetic k-means algorithm (IGKM) and constructs a fitness function defined as a product of three factors, maximization of which ensures the formation of a small number of compact clusters with large separation between at least two clusters. At last, two artificial and three real-life data sets are considered for experiments that compare IGKM with kmeans algorithm, GA-based method and genetic kmeans algorithm (GKM) by inter-cluster distance (ITD), inner-cluster distance(IND) and rate of separation exactness. The experiments show that IGKM can automatically reach the optimal value of k with high accuracy.