The morphing aircraft can independently change its aerodynamic shape to carry out wide-area glide maneuvers according to the flight mission, which greatly improves the control ability of the vehicle to the space motion trajectory, expands the inherent flight envelope of traditional aircraft, and provides a solution to the problem of cluster cooperative guidance and control of unpowered glide vehicles. In this paper, we propose an online trajectory planning method with spatio-temporal constraints to address the multi-constraint guidance problem of unpowered morphing aircraft with limited terminal time, position, and velocity. Firstly, the dynamic and kinematic models of the morphing aircraft are constructed without considering the unsteady morphing process. Based on the model prediction static programming method for spatio-temporal constraints of non-morphing aircraft, a virtual control variable representing morphable decision is introduced, and an explicit calculation method of virtual control variable is obtained. Considering the discontinuity in the morphing process of the aircraft, the time series of the virtual control variable is integrated piecewise and transformed into a morphing decision. Once the morphing decision solidifies, a model predictive static programming algorithm is employed to update guidance instructions in order to achieve omnidirectional trajectory planning with spatio-temporal constraints. The mathematical simulation demonstrates that the trajectory planning algorithm proposed in this paper exhibits strong robustness and effectively suppress terminal state dispersion, including terminal time, position, and velocity caused by uncertainty in model parameters.