The vulnerability of automated fingerprint recognition systems (AFRSs) to presentation attacks (PAs) promotes the vigorous development of PA detection (PAD) technology. However, PAD methods have been limited by information loss and poor generalization ability, resulting in new PA materials and fingerprint sensors. This article thus proposes a global-local model-based PAD (RTK-PAD) method to overcome those limitations to some extent. The proposed method consists of three modules, called: 1) the global module; 2) the local module; and 3) the rethinking module. By adopting the cut-out-based global module, a global spoofness score predicted from nonlocal features of the entire fingerprint images can be achieved. While by using the texture in-painting-based local module, a local spoofness score predicted from fingerprint patches is obtained. The two modules are not independent but connected through our proposed rethinking module by localizing two discriminative patches for the local module based on the global spoofness score. Finally, the fusion spoofness score by averaging the global and local spoofness scores is used for PAD. Our experimental results evaluated on LivDet 2017 show that the proposed RTK-PAD can achieve an average classification error (ACE) of 2.28% and a true detection rate (TDR) of 91.19% when the false detection rate (FDR) equals 1.0%, which significantly outperformed the state-of-the-art methods by ~10% in terms of TDR (91.19% versus 80.74%).