In this paper, a new non-uniform weight-updating scheme for adaptive digital beamforming (DBF) is proposed. The unique feature of the letter is that the effective working range of the beamformer is extended and the computational complexity is reduced by introducing the robust DBF based on worst-case performance optimization. The robust parameter for each weight updating is chosen by analyzing the changing rate of the Direction of Arrival (DOA) of desired signal in LEO satellite communication. Simulation results demonstrate the improved performance of the new Non-Uniform Weight-Updating Beamformer (NUWUB).