EM algorithm is an important unsupervised clustering algorithm, but the algorithm has several limitations. In this paper, we propose a fast EM algorithm (FEMA) to address the limitations of EM and enhance its efficiency. FEMA achieves low running time by combining principal component analysis(PCA), a grid cell expansion algorithm(GCEA) and a hierarchical cluster tree. PCA and multi-dimensional grid are applied to find a set of "good" initial parameters for the EM algorithm, while the hierarchical cluster tree deals with the case where the cluster is concave by making use of a merging algorithm. The experiments indicate that FEMA outperforms EM by reducing 45% of the CPU time.