In this paper, a nonlinear prediction-based control approach is proposed for stabilization of planar vertical take-off and landing (PVTOL) aircraft. This system has fewer control inputs than degrees of freedom (i.e. under-actuated) and has unstable zero dynamics (i.e. non-minimum phase). The proposed control approach is based on partial feedback linearization, which allows the emergence of a completely linearized sub-state and internal dynamics. Then, optimal trajectories are proposed for the linearized variables, where the optimization objective is to enhance the behaviour and the stability of the internal dynamics. Stability analysis of the closed-loop system is performed using a graphical tool based on Poincaré's section. The performance of the proposed scheme is illustrated through simulations.