Boost-glide vehicles are inherently under-actuated and exhibit a monotonically decreasing energy profile throughout the passive flight phase. The presence of model uncertainties, as well as deviations from expected conditions, results in significant dispersion in terminal states, which poses a considerable challenge to mission reliability. In particular, the influence of initial state dispersion at burnout and modeling errors during the glide phase can significantly affect the accuracy of terminal handover conditions. To address these challenges, a multi-constrained guidance method based on an energy reduced-order prediction model is introduced. This method leverages mechanical energy to reduce the dimensional complexity of the longitudinal dynamics, enabling a more efficient trajectory prediction. Additionally, Model Predictive Static Programming (MPSP) is utilized to reconstruct angle-of-attack profiles, ensuring precise compliance with multiple terminal constraints for the under-actuated system. The effectiveness of the proposed algorithm is validated through extensive Monte Carlo simulations, which demonstrate a significant reduction in trajectory dispersion under typical deviation conditions. These results highlight the potential for improving mission reliability and demonstrate applicability in real-world engineering scenarios involving boost-glide vehicles.