For a mission to constantly watch geostationary (Orbital inclination isn’t 0, GEO) spacecraft by an optical satellite during a whole fly-around cycle, study the relative position relationship between the two and sun during fly-around mission; design the trajectory of the optical satellite, on which, the optical satellite keeps facing to the spacecraft in the direction opposite the Sun. Firstly, for constant surveillance to geosynchronous (Orbital inclination is 0) spacecraft, study from the Keplerian orbit elements, analyze its geometric relationship with the sun and the optical satellite. Then calculate the initial phase interval that meets the requirements of the mission. Compared with Clohessy-Wiltshire equation (CW equation), this method is more concise and the spatial physical meaning is clearer. However, the orbital inclination of GEO spacecraft is usually not 0. Secondly, taking GEO spacecraft with 1° inclination as an example, calculate the initial phase interval of the mission. Thirdly, select an initial phase in the initial phase interval, and design the fly-around trajectory based on CW equation. Lastly, the optical satellite’s position when it receives the mission is initial position, and the position when the fly-around mission starts is final position. The optical satellite’s approach trajectory is summarized as spacecraft's Lambert trajectory optimization. Take the time of two orbital maneuvers as optimization variables, and the fuel consumption as optimization objective. Optimize the plan of orbital maneuvering. The total pulse thrust velocity required for orbital maneuver after optimization in the example is 18.2514m/s, which is highly feasible in engineering. This method can be used for space situational awareness and in-orbit services of GEO spacecraft.