Based on elastic aircraft, time-domain continuous gust response analysis using rational function approximation technique and time-domain discrete gust response analysis using hybrid modeling technique are presented. Two gust alleviation control schemes are designed: (1) the feedback signals are gathered by pitch rate gyroscope and accelerometers, which are located at the tip of the wing and the centroid of the aircraft, while the aileron and elevator are used as the control surfaces for gust alleviation system; (2) the feedback signal are gathered by angle of attack sensor and accelerometers which are located at the tip of the wing and the centroid of aircraft, while the aileron and elevator are used as the control surfaces for gust alleviation system. The result are demonstrated that the alleviation effect of continuous and discrete gust response by control scheme 1 and 2 satisfy the gust alleviation design target. This article are of reference value to extend gust alleviation technique to engineering application.