The universal background model (UBM) based classifiers have recently been popular for speaker recognition. In this paper, we propose a dimension reduction method using local principal component analysis to improve the performance of speaker verification systems, where maximum a Posteriori (MAP) adapted vector quantization classifier (VQ-MAP or VQ-UBM) is employed. The proposed system first partitions the UBM data into disjoint regions (clusters) via conventional VQ algorithm and PCA is performed on the set of feature vectors in each region to obtain transformation matrix. Then, multiple speaker model is constructed using the set of transformed feature vectors closest to each cluster through MAP adaptation. Conducting experiments on NIST 2001 SRE, it is shown that transforming the data onto a lower dimensional space by the proposed method improves the recognition accuracy.