The coherent Doppler wind lidar (CDWL) has long been thought to be the most suitable technique for wind remote sensing in the atmospheric boundary layer (ABL) due to its compact size, robust performance, and low-cost properties. However, as the coherent lidar exploits the Mie scattering from aerosol particles, the signal intensity received by the lidar is highly affected by the concentration of aerosols. Unlike air molecules, the concentration of aerosol varies greatly with time and weather, and decreases dramatically with altitude. As a result, the performance of the coherent lidar fluctuates greatly with time, and the detection range is mostly confined within the planetary boundary layer. The original data collected by the lidar are first transformed into a spectrogram and then processed into radial wind velocities utilizing algorithms such as a spectral centroid. When the signal-to-noise ratio (SNR) is low, these classic algorithms fail to retrieve the wind speed stably. In this work, a radial wind velocity retrieving algorithm based on a trained convolutional neural network (CNN) U-Net is proposed for denoising and an accurate estimate of the Doppler shift in a low-SNR regime. The advantage of the CNN is first discussed qualitatively and then proved by means of a numerical simulation. Simulated spectrum data are used for U-Net training and testing, which show that the U-Net is not only more accurate than the spectral centroid but also achieves a further detection range. Finally, joint observation data from the lidar and radiosonde show excellent agreement, demonstrating that the U-Net-based retrieving algorithm has superior performance over the traditional spectral centroid method both in accuracy and detection range.