This paper addresses the problem of simultaneously constraining impact time and impact angle during terminal missile guidance under varying missile speed. A spatio-temporal constraint guidance law with high accuracy and robustness is proposed for use when the missile’s speed varies. First， based on existing proportional-navigation expressions for the predicted remaining flight-path length and impact angle， the desired velocity-lead angle that satisfies the spatio-temporal constraints is solved. Second， the error in the velocity-lead angle is taken as a sliding surface and， by means of sliding-mode control， a bias term is constructed on top of the proportional-navigation law； this yields a spatio-temporal guidance law that， in the speed-controllable case， avoids command singularities and abrupt command changes and achieves simultaneous control of impact time and impact angle. Next， a predictive estimation algorithm for the desired velocity-lead angle with respect to impact time is presented to extend the pro-posed guidance law to scenarios with uncontrollable speed； an optimized command-update strategy is also designed to prevent computational latency from degrading the command update cycle. Finally， numerical simulations demonstrate that the proposed guidance law attains the desired impact time and impact angle under speed variations and stochastic disturbances， validating its high guidance accuracy and good robustness in complex environments.