Gabor features have been known to be effective for face recognition. However, only a few approaches utilize phase feature and they usually perform worse than those using magnitude feature. To investigate the potential of Gabor phase and its fusion with magnitude for face recognition, in this paper, we first propose local Gabor XOR patterns (LGXP), which encodes the Gabor phase by using the local XOR pattern (LXP) operator. Then, we introduce block-based Fisher's linear discriminant (BFLD) to reduce the dimensionality of the proposed descriptor and at the same time enhance its discriminative power. Finally, by using BFLD, we fuse local patterns of Gabor magnitude and phase for face recognition. We evaluate our approach on FERET and FRGC 2.0 databases. In particular, we perform comparative experimental studies of different local Gabor patterns. We also make a detailed comparison of their combinations with BFLD, as well as the fusion of different descriptors by using BFLD. Extensive experimental results verify the effectiveness of our LGXP descriptor and also show that our fusion approach outperforms most of the state-of-the-art approaches.