Solar Sail applications utilizing the advantages of propellant-free and theoretically infinite specific impulse are widely investigated, especially for interplanetary/interstellar and near-Earth asteroid missions and non-Keplerian orbit designs. However, applications regarding to the Low Earth Orbit (LEO), specifically below 700 km, are rarely studied as aerodynamic drag is dominant. This study is aimed to harvest the LEO mission advantages by proposing an elliptical orbit design and control via continuous low thrust. Two-tier mode based control algorithm is employed and maximum energy gain or loss thrust vector control is implemented depending on the phase of the mission, i.e. raising or decreasing. It is shown that the proposed mission orbit and successive low thrust maneuvers are applicable. The results depending on the initial orbit and satellite parameters are also investigated.