To solve the problems of nonlinearity and obviously changed manipulating efficiency in flight of UAV, a longitudinal control law is designed for a Flying-wing UAV, which is the integrating of Robustness Servomechanism Linear Quadratic Regulator(RSLQR) and L1 adaptive control method.The controlled variable is chosen as C*, which is a combination of longitudinal acceleration and pitch rate.The baseline controller is based on RSLQR method to fit the control requirement of the UAV.The controller is augmented by L1 adaptive output feedback structure to maintain the desired close-loop system characteristics in the presence of the aerodynamic uncertainties and the significant change of the elevator coefficient caused by the transformation of flight state.This paper summarizes the theory, the design, simulation testing and flight test results using a RSLQR-L1 method, which validates the performance and the robustness of the designed control system.