Historical documents contain essential information about the past, including places, people, or events. Many of these valuable cultural artifacts cannot be further examined due to aging or external influences, as they are too fragile to be opened or turned over, so their rich contents remain hidden. Terahertz (THz) imaging is a nondestructive 3D imaging technique that can be used to reveal the hidden contents without damaging the documents. As noise or imaging artifacts are predominantly present in reconstructed images processed by standard THz reconstruction algorithms, this work intends to improve THz image quality with deep learning. To overcome the data scarcity problem in training a supervised deep learning model, an unsupervised deep learning network (CycleGAN) is first applied to generate paired noisy THz images from clean images (clean images are generated by a handwriting generator). With such synthetic noisy-to-clean paired images, a supervised deep learning model using Pix2pixGAN is trained, which is effective to enhance real noisy THz images. After Pix2pixGAN denoising, 99% characters written on one-side of the Xuan paper can be clearly recognized, while 61% characters written on one-side of the standard paper are sufficiently recognized. The average perceptual indices of Pix2pixGAN processed images are 16.83, which is very close to the average perceptual index 16.19 of clean handwriting images. Our work has important value for THz-imaging-based nondestructive historical document analysis.