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An adaptive autopilot is presented for the pitch and yaw channels of a guided spinning rocket. Firstly, the uncertain dynamic model of a guided spinning rocket is established, which is used to evaluate the performance of the proposed adaptive autopilot. Secondly, a robust adaptive output feedback autopilot containing a baseline component and an adaptive component is designed. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. A simple design procedure based on linear matrix inequality is proposed that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated. Finally, numerical simulations are performed to evaluate the robustness and tracking performance of the proposed robust adaptive autopilot. The simulation results showed that the robust adaptive output autopilot can achieve asymptotic command tracking with significant uncertainty in control effectiveness, moment coefficient, and measurement noise.