Up to now it is the duty of ground satellite control centers to provide daily operation services for on-orbit GEO satellites. With the evolution in technologies and human cognition, if an on-orbit GEO satellite can take over the task by itself, it will dramatically reduce the burden borne by the ground, along with improving its independent survivability and lowering the entire system operation cost, perhaps being the trend of future on-orbit satellite management. This paper presents daily operation items of a typical on-orbit GEO satellite and studies algorithms which are used to perform them. Then the possibility of autonomy for an on-board satellite is discussed. The result manifests that it is highly likely for a satellite to manage itself in a period without attendance from the ground. Finally we design an autonomy prototype which is capable of performing daily operations by a satellite itself. To solve the problems and lower risks caused by autonomy, some counter measures are presented here. Our study shows that it is feasible, based on currently satellite manufacture technologies and control experience, to produce such satellites with autonomous operation capacity. It may be an effective way to solve the dilemma between the tough tasks caused by on-orbit satellite rapid growth and the resource shortage of ground satellite control systems.