An optimal strategy based on minimum control effort with terminal position constraint is developed for an exoatmospheric interceptor with a fixed-interval guidance time. It is then integrated with sliding-mode control theory to drive an optimal sliding-mode guidance law for fixed-interval guidance time. In addition, this guidance law is generalized for intercepting an arbitrarily time-varying target maneuver. Robustness of the new guidance method against disturbances and good miss distance performance are proved by second method of Lyapunov and simulation results. The presented guidance law is simple to implement in practical applications