This article reports a new clustering method based on the k-means algorithm to high-dimensional gene expression data. The proposed approach makes use of bidirectional penalties to constrain the number of clusters and centroids of clusters to simultaneously determine the unknown number of clusters and handle large amounts of noise in gene expression data. Numeric studies indicate that this algorithm not only performs better in clustering but is also comparable to other approaches in its ability to obtain the correct number of clusters and correct signal features. Finally, we apply the proposed approach to analyze two benchmark gene expression datasets. These analyses again indicate that the proposed algorithm performs well in clustering high-dimensional gene expression data with an unknown number of clusters.