The flight of Manned Maneuvering Unit （MMU） carrying an astronaut above lunar surface contains climbing turn segment， cruise flight segment， and turning down segment. The paper studied the trajectory and main engine’s thrust optimization problem aiming at the lowest fuel consumption for the climbing turn segment. Firstly， Pontryagin Minimum Principle was used to derive the optimal function forms of magnitude and direction angle of main engine’s thrust. Theoretical analysis demonstrated that the engine should work in switch mode with at most one switching， meanwhile the cotangent function of direction angle was an affine function of time. Therefore the engine’s optimal thrust function can be determined by four parameters， which are duration times of “on” and “off’， slope and intercept parameters of the affine function mentioned above. The climbing turn segment was needed to transition smoothly to the cruise flight segment，thus the terminal flight states of MMU in climbing turn segment are required to meet three pre-assigned parameter values ， i.e.， flight height， flight velocities magnitude and direction. Then the optimal control problem with the lowest fuel consumption was transformed to a nonlinear programming problem involving four variables and three equality constraints. One design freedom was left， meaning that solution can be obtained easily by one-dimensional search. The effectiveness of the proposed method is verified by numerical simulations.