Approaching observation is a new way of space-based inspection. Precisely steering the flight vehicle to the observing point near the target is one of the key technologies. An optimal terminal guidance is presented for the terminal approaching. Firstly, the process of approaching observation is transformed to an optimal control problem by founding equations of relative motion in inertial coordinate systems and performance index which synthesizes the fight time and fuel consuming. Then optimal thrust direction, nozzle working hours, and time-to-go are derived, based on which a scheme of optimal guidance is designed. Finally, simulations are conducted and results demonstrate that the guidance algorithm can meet the requirements of approaching observation mission with the high precision. The study herein also is helpful to deep space exploration, rendezvous and docking.