Wave-encoded single-shot fast spin echo imaging (SSFSE) achieves good structural delineation in less than a second while its calibration and reconstruction usually take more than a minute to finish. This study proposes a method to accelerate the calibration and reconstruction for wave-encoded SSFSE with a deep-learning-based approach. This method first learns the systematic imperfections with a deep neural network, and then reconstructs the image with another unrolled convolutional neural network. The proposed approach achieves 2.8-fold speedup compared with conventional approaches. Further, it can also reduce the ghosting and aliasing artifacts generated in conventional calibration and reconstruction approaches.