A fuel-optimal trans-Earth trajectory design for manned lunar missions is presented. The gravitational effects of the Moon, Earth, and Sun constitute a 4-body problem. Imposing maximum thrust, fuel budget, and flight time as design constraints, we formulate a nonlinear constrained fuel-optimal control problem to obtain an optimal trajectory from a low lunar parking orbit to an Earth interface condition. The resulting optimal control problem is solved using Legendre pseudospectral method. An anti-aliasing method based on Bellman's principle of optimality is employed to test and improve the accuracy of the solution. All results are developedn and obtained using the software package DIDO ©.