Emerging 3D fingerprint recognition technologies have attracted growing attention in addressing the limitations from contact-based fingerprint acquisition and improve recognition accuracy. However, the complex 3D imaging setups employed in these systems typically require structured lighting with scanners or multiple cameras which are bulky with higher cost. This paper presents a more accurate and efficient 3D fingerprint identification approach using a single 2D camera with multiple colored LED illumination. A 3D minutiae tetrahedron based algorithm is developed to more efficiently match recovered minutiae features in 3D space and address the limitations of 3D minutiae matching approach in the literature. This algorithm significantly improves the matching time to about 15 times than the state-of-art in the reference. A hierarchical tetrahedron matching scheme is also developed to further improve the matching accuracy with faster speed. The 2D images acquired to reconstruct the 3D fingerprints are also used to recover 2D minutiae and further improve matching performance for 3D fingerprints. A new two-session database acquiring from 300 different clients consists of 2760 3D fingerprints reconstructed from 5520 colored 2D fingerprints is also developed and shared in public domain to further advance much needed research in this area. Extensive experimental results presented in this paper validate our approach and demonstrate the effectiveness of proposed algorithms.