This paper focuses on a round-trip trajectory design for solar sailing exploration. Recently, round-trip sample return missions are gathering strong attention owing to the great achievement by Hayabusa. While, solar sailing technology is now developing, which is a technology to obtain acceleration by making use of solar radiation pressure, and is regarded as an efficient technology for the deep-space exploration. And currently there can be expected a plan of Deep Space Port around L2 point in the Sun-Earth system; it will make solar sailing exploration efficient. In this context, the objective of this study is designing and investigating the round-trip exploration trajectory originating from and ending at L2 point. The whole sequence is divided into several phases, and each of them is optimized. This trajectory design method is useful for asteroid fly-by and sample return missions. Besides, station keeping orbits around L2 point are designed. Two kinds of control are considered; attitude control and spin rate control, and both proved to be available for making the periodic orbit. Although the designed orbits are unstable, a stabilization method based on feedback control is established in this paper. Both direct control of the attitude and attitude control via only spin rate control stabilize the periodic orbit.