Fingerprint pose estimation is a challenging problem since the pose is not defined by salient anatomical features and fingerprint images usually suffer from noise and small area. In this article, we proposed a method for joint estimation of pose and singular points of fingerprints, with the expectation that the pose and singular points can improve each other. By virtue of that singular points can be located accurately, we hope to improve the accuracy of pose estimation. Meanwhile, the robustness of pose estimation can improve the anti-noise performance of singular point detection. To achieve this, we propose a multi-task deep neural network, which contains a feature extraction body and two estimation heads for singular point and pose respectively. The proposed network can deal with various types of fingerprints, including plain, rolled and latent fingerprints. Experiments on four databases (NIST SD4, SD14, SD27 and FVC2004 DB1A) show that (1) the estimated poses and detected singular points are close to manual annotations despite of different image qualities; (2) the estimated poses for mated fingerprint pairs are consistent; and (3) the proposed pose estimation method outperforms state-of-the-art methods while utilized as pose constraint for a fingerprint indexing algorithm.