This paper presents a new type of guidance law for homing missiles. The design concept is based upon the minimization of time duration for homing. It is shown that to realize this guidance concept an algorithm to predict the collision course and a guidance command generator to turn the heading of the missile toward the direction of the predicted collision course are necessary. A prediction algorithm for the collision course is derived and the realized overall guidance law is shown to be easily implementable. Simulation results are given to demonstrate the minimum time behavior and the widened launching envelope.