Minimum-fuel, planar trajectories from a circular low Earth parking orbit to a circular low lunar parking orbit with a fixed thrust-coast-thrust engine sequence are computed for a low-thrust spacecraft. The problem is studied in the context of the classical restricted three-body problem. Since a low-thrust trajectory is a long-duration transfer with slowly developing spirals about Earth and the moon, the minimum-fuel Earth-moon trajectory is obtained by formulating and successively solving a hierarchy of three subproblems. This three-stage approach presents a systematic and effective method for solving the complex and numerically sensitive minimum-fuel, lowthrust, trajectory problem. The first subproblem is to obtain several optimal continuous-thrust Earth-escape and moon-capture trajectories. The second subproblem is to compute a suboptimal, all-coasting, translunar trajectory between boundary conditions provided by the first subproblem. Finally, the complete minimum-fuel trajectory problem is solved using a direct/indirect method. The hybrid method utilizes the costate time histories to parameterize the thrust steering history. Numerical results are presented for the optimal Earth-moon trajectories.