The performance of conventional minutiae-based fingerprint authentication algorithms degrades significantly when dealing with low quality fingerprints with lots of cuts or scratches. A similar degradation of the minutiae-based algorithms is observed when small overlapping areas appear because of the quite narrow width of the sensors. Based on the detection of minutiae, Scale Invariant Feature Transformation (SIFT) descriptors are employed to fulfill verification tasks in the above difficult scenarios. However, the original SIFT algorithm is not suitable for fingerprint because of: (1) the similar patterns of parallel ridges; and (2) high computational resource consumption. To enhance the efficiency and effectiveness of the algorithm for fingerprint verification, we propose a SIFT-based Minutia Descriptor (SMD) to improve the SIFT algorithm through image processing, descriptor extraction and matcher. A two-step fast matcher, named improved All Descriptor-Pair Matching (iADM), is also proposed to implement the 1:N verifications in real-time. Fingerprint Identification using SMD and iADM (FISiA) achieved a significant improvement with respect to accuracy in representative databases compared with the conventional minutiae-based method. The speed of FISiA also can meet real-time requirements.