As an important feature, orientation field describes the global structure of fingerprints. It provides robust discriminatory information other than traditional widely-used minutiae points. However, there are few works explicitly incorporating this information into fingerprint matching stage, partly due to the difficulty of saving the orientation field in the feature template. In this paper, we propose a novel representation for fingerprints which includes both minutiae and model-based orientation field. Then, fingerprint matching can be done by combining the decisions of the matchers based on the global structure (orientation field) and the local cue (minutiae). We have conducted a set of experiments on large-scale databases and made thorough comparisons with the state-of-the-arts. Extensive experimental results show that combining these local and global discriminative information can largely improve the performance. The proposed system is more robust and accurate than conventional minutiae-based methods, and also better than the previous works which implicitly incorporate the orientation information. In this system, the feature template takes less than 420 bytes, and the feature extraction and matching procedures can be done in about 0.30 s. We also show that the global orientation field is beneficial to the alignment of the fingerprints which are either incomplete or poor-qualitied.