With the rapid development of the image generation technologies, the malicious abuses of the GAN-generated fingerprint images poses a significant threat to the public safety in certain circumstances. Although the existing universal deep forgery detection approach can be applied to detect the fake fingerprint images, they are easily attacked and have poor robustness. Meanwhile, there is no specifically designed deep forgery detection method for fingerprint images. In this paper, we propose the first deep forgery detection approach for fingerprint images, which combines unique ridge features of fingerprint and generation artifacts of the GAN-generated images, to the best of our knowledge. Specifically, we firstly construct a ridge stream, which exploits the grayscale variations along the ridges to extract unique fingerprint-specific features. Then, we construct a generation artifact stream, in which the FFT-based spectrums of the input fingerprint images are exploited, to extract more robust generation artifact features. At last, the unique ridge features and generation artifact features are fused for binary classification (\textit{i.e.}, real or fake). Comprehensive experiments demonstrate that our proposed approach is effective and robust with low complexities.