To reduce the high dimensionality required for training of feature vectors in speaker identification, we propose an efficient GMM based on local PCA with Fuzzy clustering. The proposed method firstly partitions the data space into several disjoint clusters by fuzzy clustering, and then performs PCA using the fuzzy covariance matrix in each cluster. Finally, the GMM for speaker is obtained from the transformed feature vectors with reduced dimension in each cluster. Compared to the conventional GMM with diagonal covariance matrix, the proposed method needs less storage and shows faster result, under the same performance.