The terminal phase of an encounter between an anti-ballistic missile and a re-entry warhead, which performing a random bang-bang evasive maneuver, was addressed. The missile uses a guidance law derived from linear differential game theory (DGL), which is implemented by using an interacting multiple model algorithm (IMM). Compared with the methods used before, the proposed algorithm not only substantially decreases the computational load, but also improves guidance accuracy. Monte Carlo simulations show that the DGL/IMM algorithm performs well even if the target maneuver model is unknown to the guidance system.