A compact airborne coherent Doppler lidar (ACDL) was developed by Ocean University of China. The system design, methods of motion compensation, velocity correction and wind inversion have been explained in this paper. The data analyzed in this paper are based on the first domestic UAV-borne Doppler lidar experiment for offshore wind at Hailing Island, Guangdong Province in 2016. The reliability of correction and inversion algorithms have been proved with ground-based Doppler lidar. ACDL has been proved to be an effective tool to achieve offshore wind observation.