In order to enable clustering to be done under a lower dimension, a new feature selection method for clustering is proposed. This method has three steps which are all carried out in a wrapper framework. First, all the original features are ranked according to their importance. An evaluation function E(f) used to evaluate the importance of a feature is introduced. Secondly, the set of important features is selected sequentially. Finally, the possible redundant features are removed from the important feature subset. Because the features are selected sequentially, it is not necessary to search through the large feature subset space, thus the efficiency can be improved. Experimental results show that the set of important features for clustering can be found and those unimportant features or features that may hinder the clustering task will be discarded by this method.