This manuscript investigates a multi-stage cooperative interception problem in which a group of flight vehicles are launched successively to cooperatively intercept a high maneuvering target. First, the multi-stage cooperative interception problem is formulated. Due to the measurement noise and uncertainties, a dynamic distribution is used to describe the location of the target which can be obtained by Kalman filter. A coverage-based algorithm is proposed to obtain the expected locations of the flight vehicles by maximizing the interception probability. Moreover, the guidance control law of each flight vehicle is given based on the classical optimization approach.