The linear-quadratic-Gaussian (LQG) control synthesis has the advantage of dealing with the uncertain linear systems disturbed by additive white Gaussian noise while having incomplete system state information available for control-loop feedback. This paper hence explores the feasibility of designing and implementing a stability augmentation autopilot for fixed-wing unmanned air vehicles using the LQG approach. The autopilot is composed of two independently designed LQG controllers which control the longitudinal and lateral motions of the aircraft respectively. The corresponding linear models are obtained through a system identification routine which makes use of the combination of two well-established identification methods, namely the subspace method and prediction error method. The two identification methods complement each other well and this paper shows that the proposed system identification scheme is capable of attaining satisfactory state-space models. A complete autopilot design procedure is devised and it is shown that the design process is simple and effective. Resulting longitudinal and lateral controllers are successfully verified in computer simulations and actual flight tests. The flight test results are presented in the paper and they are found to be consistent with the simulation results.