A deep learning-enhanced holographic wavefront sensor (DLHWS) is proposed to overcome the limitations of conventional holographic modal wavefront sensors (HMWS). Traditional HMWS, based on the second-moment-intensity (SMI-HMWS), suffers from measurement inaccuracies due to speckle noise from kinoform computer-generated holograms (CGHs) and restricted measurable modes. The DLHWS utilizes deep neural networks to process multiple biased images generated by a CGH, either a lightweight convolutional neural network (CNN) for modal coefficient estimation (DLHWS-c) or a UNet for direct phase map reconstruction (DLHWS-p). Simulations and experiments demonstrate that DLHWS significantly improves wavefront sensing accuracy and capability to detect high-order aberrations. DLHWS-c offers superior inference speed and high accuracy for low-order modes. In contrast, DLHWS-p delivers higher precision in capturing high-order aberrations comprising hundreds of modes induced by atmospheric turbulence but requires greater computational resources.