In this paper, low thrust spacecraft trajectory optimization for the lunar capture trajectory in the circular restricted threebody problem (CRTBP) is presented. Explanations of the controlled motion of the satellite under the dynamics of CRTBP are presented with the application of the Hills region and Jacobi constant in the trajectory optimization. The initial orbit of the spacecraft of interest is assumed to be a geosynchronous transfer orbit (GTO) with a semi-major axis of 43444km and eccentricity of 0.8.