This paper proposes an algorithm to deal with the feature selection in Gaussian mixture clustering by an iterative way: the algorithm iterates between the clustering and the unsupervised feature selection. First, we propose a quantitative measurement of the feature relevance with respect to the clustering. Then, we design the corresponding feature selection scheme and integrate it into the Rival Penalized EM (RPEM) clustering algorithm (Cheung 2005) that is able to determine the number of clusters automatically. Subsequently, the clustering can be performed in an appropriate feature subset by gradually eliminating the irrelevant features with automatic model selection. Compared to the existing methods, the numerical experiments have shown the efficacy of the proposed algorithm on the synthetic and real world data.