The time delay of seekers has grown to be a serious issue for tactical missile guidance with the development of flight vehicle technologies. To address the problem, a measurement compensation system for the seeker, with lags and delays based on predictive active disturbance rejection control, is proposed. In addition, to eliminate the effects of target maneuvers to the tactical missile guidance, an adaptive finite-time convergent sliding mode guidance law, based on super-twisting algorithm, is proposed in three-dimensional missile-target engagement kinematics. Specifically, the compensation system consists of a predictive tracking structure and an active disturbance rejection control system, which could follow a virtual measurement without lags and delays. The compensation system has advantages in disturbance rejection and model inaccuracy addressing, compared with existing compensation methods for seeker measurement. As for the sliding mode guidance law design, the proposed approach is based on an improved super-twisting algorithm with fast convergent adaptive gains, which has advantages in addressing unknown but bounded target maneuvers and avoiding chattering of the classical sliding mode control. As a result, the measurement compensation system and the adaptive sliding mode guidance law is verified robust and effective under the proposed constraints by the simulation examples.