For manned lunar and deep space exploration missions in the future, the transfer design of low energy round trip circumlunar orbit and libration point in the Earth Moon system is studied, the effect of circumlunar orbit changes on key parameters such as flight time and mission fuel consumption are systematically analyzed under different three body orbits, and a search strategy for the initial value of round trip orbit design is presented. In order to solve the problem of initial value sensitivity of design variables, a differential correction algorithm is used to rapidly construct the initial transfer orbit by combining the invariant manifold with the characteristics of the libration point orbit. Considering multiple constraints such as near lunar and optimal fuel simultaneously, the round trip trajectory between the circumlunar orbit and libration point orbit is further studied through the multiple shooting method and quadratic programming algorithm, and the gradient formula of the constraint equations is deduced to improve the design efficiency. In order to analyze the characteristics of round trip orbits and verify the effectiveness of the design strategy, the relationship between the variation of parameters, such as amplitude of three body orbits, the inclination of different circumlunar orbits, and the transfer time and fuel consumption is studied. The design results have important reference significance for the design of round trip orbits and selection of parameters for the deployment of lunar exploration vehicles.