Recent years have witnessed a growing interest in developing automatic palmprint recognition methods. Most of the previous works have focused on two dimensional (2D) palmprint recognition in the past decade. However, 2D palmprint images could be easily forged or affected by noise, causing potential security risks for practical applications. Therefore, three dimensional (3D) palmprint recognition has been regarded as a promising way to further improve the performance of palmprint recognition systems. In this paper, we have proposed an efficient 3D palmprint recognition method by using local texture feature sets. We first employ shape index representation to demonstrate the geometry characteristics of local regions in 3D palmprint data. Then, we incorporate rich local texture cues from two complementary sources-local ternary pattern (LTP) and Gabor wavelet to extract features from the shape index image-proving that the combination is more accurate than either feature set alone, and finally fuse them at a matching score level. Further experiments on Hong Kong Polytechnic University 3D palmprint database validate that our method outperforms existing state-of-the-art methods in terms of recognition accuracy, showing the effectiveness of our method.