Intercepting an incoming ballistic missile with another missile is a well-known control problem. Making such an intercept in a head-on configuration is, however, a more difficult task with traditional techniques such as proportional navigation. A head-on intercept is desirable under some conditions since it maximizes the probability of destroying the incoming missile warhead. This paper presents a novel approach to this problem using fuzzy logic control methods. The approach uses two inputs and a fuzzy logic inference scheme to generate the control output. The fuzzy inputs are the respective angles of the interceptor and target velocity vectors relative to the line of sight between the two missiles. The output is the change in the interceptor acceleration direction to accomplish the desired intercept. For a realistic simulation of missile kinematics and radar measurement errors, this fuzzy logic system guided the interceptor to accurate head-on missile intercepts. Over a wide range of incoming missile parameters, it achieved intercepts to within one meter, deviating from head-on by less than one degree. Details of the approach used and typical performance results of the model will be presented.