Directional warhead technology is a new killing technology that uses target miss direction information to change the blasting direction through the change of missile body or the logic control of warhead initiation to achieve the maximum damage effect. It is also one of the key promising technologies for the future new generation of air-defense missiles to achieve capability leaping. The overall design problems of the aimed killing air-defense missile equipped with a directional warhead are studied. Firstly, a prediction method of miss information that compensates the missile acceleration for aimed killing air-defense missiles is proposed. The demand for acquiring miss information in advance is met. Secondly, the distributing regularity of the predicted impacting point and the formation mechanism of fuzzy prediction are studied, which provides theoretical support for solving the fuzzy problem. Thirdly, the aiming accuracy improvement methods for small miss distance encounter cases are studied. Finally, the simulations taking a certain type of aimed killing air-defense missile as examples are conducted.