In this paper, a method of GB2DPCA+PCA which is a bi-directional compressed 2DPCA (B2DPCA) plus PCA method by integrating the Gabor wavelet representation of palm images is proposed. The 2DPCA is a two dimensional principal component analysis method. In this approach, the Gabor wavelets are used to extract palmprint features. The B2DPCA is applied directly on the Gabor transformed matrices to remove redundant information from the image rows and columns and PCA is used to further reduce the dimension. The proposed GB2DPCA+PCA yields greater palmprint recognition accuracy while reduces the dimension. The effectiveness of the proposed algorithm is also verified using the PolyU palmprint databases.