In this paper we develop a novel learning-based approach for mobile distributed beamforming without channel state information. We consider narrowband beamforming between a mobile UAV group and a base station under limited feedback, and propose a graph recurrent neural network (GRNN) approach to leverage local collaboration among the UAVs. The GRNN method is shown to be robust to variations in UAV speeds and group heading, and scales with the UAV group size. We compare to codebook and binary feedback methods and show that better performance is achieved with the proposed GRNN method.