One of the open problems of modern data mining is clustering high dimensional data. For this in the paper a new technique called GAHDClustering is proposed, which works in two steps. First a GA-based feature selection algorithm is designed to determine the optimal feature subset; an optimal feature subset is consisting of important features of the entire data set next, a K-means algorithm is applied using the optimal feature subset to find the clusters. On the other hand, traditional K-means algorithm is applied on the full dimensional feature space. Finally, the result of GA-HDClustering is compared with the traditional clustering algorithm. For comparison different validity matrices such as Sum of squared error (SSE), Within Group average distance (WGAD), Between group distance (BGD), Davies-Bouldin index(DBI), are used .The GA-HDClustering uses genetic algorithm for searching an effective feature subspace in a large feature space. This large feature space is made of all dimensions of the data set. The experiment performed on the standard data set revealed that the GA-HDClustering is superior to traditional clustering algorithm.