A parameter-varying, model-predictive envelope protection system is developed simplifying the controller structures required to keep the aircraft within a safe angle-of-attack and normal load factor envelope. The idea of a quasi-steady flight condition is used to map the flight envelope limits onto the setpoint values of a single flight control law. Since no mode switching is required, the selected level of automation, i.e., autopilot and flight management functionalities, is independent from the proximity to any angle-of-attack and normal load factor limit. In contrast to previous approaches, the proposed algorithm makes use of a quasi-linear, parameter-varying control loop model to adapt to the true nonlinear aircraft behavior. A variance-based sensitivity analysis highlights the most significant scheduling variables within this control loop model and, therefore, indicates the option of model reduction and improvement in efficiency, respectively. The proposed envelope protection system is evaluated throughout virtual flight tests with the unmanned flight test platform ULTRA-Dimona showing promising overall performance also in the presence of wind and turbulence.