This paper deals with the preview gust alleviation control system of an aircraft, which mitigates dangerous vertical acceleration due to wind gust using the forward wind velocity measured by the LIDAR (LIght Detection And Ranging). Although the vertical acceleration can be alleviated by preview control, the preview feedforward part tends to be sensitive to measurement errors. In order to maintain consistently high acceleration alleviation performance, the preview feedforward needs to be robust to errors. This paper presents a design method for preview feedforward gains that can reduce the effect of measurement errors. Nonlinear simulation results of a small jet aircraft are provided to show that the designed preview control gain can both alleviate vertical acceleration and be robust against random and bias errors.