With the fast development in aeronautical technology, aircraft is evolving toward a wider speed ranging from subsonic, transonic, and supersonic to hypersonic speeds. The variable-sweep-wing morphing waverider provides an effective way to meet the demanding wide-speed and long-range flight requirements. However, the special morphing mechanism, variable stability margin, and the aerothermal heating of the morphing waverider, altogether impose difficulties and challenges on its flight tracking control problem, especially under parameter uncertainties, input saturation, and state constraints. To handle this issue, a six degrees of freedom barrier Lyapunov function (BLF) based nonlinear model predictive controller (NMPC) consisting of two loops is proposed in this article based on the control-oriented model of a symmetric-sweep-wing morphing waverider. Specifically, a virtual control signal of three-axis angular rates is provided by the BLF-based outer-loop NMPC to not violate the flight constraints, combined with an auxiliary system according to the desired angle of attack, sideslip angle, and bank angle. Then, the desired virtual control signal is modified by a saturation function and a first-order command filter, and the control commands are generated by the BLF-based inner-loop NMPC to deal with the input saturation by an auxiliary system. Meanwhile, a nonlinear disturbance observer is applied to estimate the morphing moments considering parameter uncertainties. The stability of the overall closed-loop system is analyzed by the Lyapunov stability theory. Finally, the performance of the controller is investigated via extensive and comparative numerical simulations.