A joint Doppler shift and channel estimation method for the millimeter-wave communication system of an unmanned aerial vehicle (UAV) equipped with a large-scale uniform linear antenna (ULA) array has been proposed. Since Doppler shift induces intercarrier interference, the parameters of the channel paths have been decomposed into the Doppler shift and the channel information. In order to obtain the Doppler shift, a new estimation algorithm based on a combination of discrete Fourier transform and phase rotation has been proposed, which can determine the appropriate number of antennas. In addition to estimating the channel information, a low-complexity joint Doppler shift and channel estimation method has been designed that can quickly obtain accurate estimates. Furthermore, the achievable sum rate, the theoretical bounds of the mean squared errors, and the Cramér-Rao lower bounds of the estimation method have been derived. The analysis and simulation results prove that the performance of the proposed approach is close to the theoretical inference.