Aiming at terminal guidance law design of airborne boost-phase ballistic missile interception under acceleration of target without availability, we study on optimal sliding-mode terminal guidance law design of Kinetic-Kill Vehicle. Motion characteristic and infrared characteristic of ballistic missile are analyzed basing on founding ballistic missile boost-phase motion equations. Optimal terminal guidance law of Kinetic-Kill Vehicle is designed basing on undershoot quantity least and energy minimum. Optimal guidance law and augmented proportional navigation law having the same form is proved in theory. Optimal sliding-mode terminal guidance law is designed under acceleration of target without availability, using optimal control theory and sliding-mode control theory. Simulation show that optimal sliding-mode terminal guidance law satisfies required index, reaching the aim to direct hit the target. The correctness and effectiveness of the optimal sliding-mode guidance law are proved.