This paper aims to propose a nonlinear autopilot for hypersonic vehicles that undergo aerodynamic-propulsion dynamics couplings. Based on the dynamic characteristics of hypersonic vehicles, a cascade autopilot structure is considered using the approximation of the time-scale separation. The approximated dynamics are derived to apply the nonlinear control approach, especially the feedback linearization control. The desired error dynamics are adopted as specific forms to enforce the resultant autopilot structure to become the three-loop structure. In this way, the proposed autopilot can fully exploit the favorable features of the three-loop autopilot: ensuring a good tracking performance in the presence of model uncertainties while handling nonlinear dynamics. Theoretical analysis and numerical simulations verify that the proposed autopilot can compensate for the uncertainty source from the aerodynamic-propulsion interactions effectively.