This paper deals with the nonlinear autopilot design for spaceplanes based on the three-loop autopilot architecture. To this end, the nonlinear dynamics equations for spaceplanes during the reentry phase are first determined. The dynamic characteristics of the dynamics model are then investigated. The analysis results show that the time-scale separation is valid in the autopilot design for spaceplanes. Accordingly, based on the approximation of the time-scale separation, the proposed autopilot is designed by leveraging the feedback linearization control technique in conjunction with specific forms of the desired error dynamics. The key feature of the proposed autopilot lies in the fact that the resultant autopilot is given by the nonlinear three-loop autopilot structure, which has been widely applied to various flight vehicles. Thus, favorable characteristics of the three-loop autopilot are inherited. Numerical simulations verify our findings in this study.