This paper presents a gain-scheduled design for a missile longitudinal autopilot. The gain-scheduled design is novel in that it does not involve linearizations about trim conditions of the missile dynamics. Rather, the missile dynamics are brought to a quasi-linear parameter varying (LPV) form via a state transformation. An LPV system is defined as a linear system whose dynamics depend on an exogenous variable whose values are unknown a priori but can be measured upon system operation. In this case, the variable is the angle-of-attack. This is actually an endogenous variable, hence the expression ``quasi-LPV''. Once in a quasi-LPV form, a robust controller using μ-synthesis is designed to achieve normal acceleration control via fin deflections. The final design is an inner/outer loop structure, with angle-of-attack control being the inner-loop, and normal-acceleration control being the outer loop.