Pure shift methods improve the resolution of proton nuclear magnetic resonance spectra at the cost of time. The pure shift yielded by chirp excitation (PSYCHE) method is a promising pure shift method. We propose a method of reconstructing the undersampled PSYCHE spectra based on deep learning to accelerate the spectra acquisition. It only takes 17 s to obtain a high-quality pure shift spectrum. The network can completely remove undersampling artifacts and chunking sidebands and improve the signal-to-noise ratio, obtaining completely clean pure shift spectra. The reconstruction quality is better than the iterative soft thresholding method. In addition, the network can differentiate low-level signals and chunking sidebands with similar intensities in the mixture, remove sidebands, and retain signals, promoting correct mixture analysis.