For the problem of intercepting a high-speed large maneuvering target with an accelerating missile， it is assumed that the missile has constant axial acceleration and adjusts its acceleration direction by controlling the attack angle. Assuming that the target exhibits a constant lateral maneuver， this paper proposes an accurate time-to-go estimation method. The sliding mode surface is designed so that the missile first corrects the initial heading error and then flies in a straight line to the target. A non-homogeneous disturbance observer is introduced to quickly estimate the acceleration of the target. A super-twisting algorithm is applied to implement the guidance law. The finite-time stability of the proposed guidance law is proved. Through the simulation comparison with the guidance to collision law， it is verified that the proposed guidance law improves the capture area of the missile. It can intercept the target whose maneuvering ability is close to that of the missile when the initial heading error is small.