This paper deals with missile autopilot design for agile turn phase in air-to-air engagement scenarios. To attain a fast response, angle-of-attack (AOA) is adopted for an autopilot command structure. Since a high operational AOA is generally required during the agile turn phase, dealing with the aerodynamic uncertainties can be a challenge for autopilot design. As a remedy, a new controller design method based on robust nonlinear control methodology such as time delay control is proposed in this paper. Nonlinear observer is also proposed to estimate the AOA in the presence of the model uncertainties. The performance of the proposed controller with variation of the aerodynamic coefficients is investigated through numerical simulations.