In this thesis, minimum-fuel, trajectory optimization from a parking orbit considering the landing site is dealt with for a soft lunar landing. The landing site is determined by the terminal longitude and latitude and those parameters are important factors to design the precise landing trajectory. The analysis of the trajectory and control time histories, which are obtained from the optimization results considering the landing site, could be applied to other analyses such as divert capability, cross range capability, etc. The trajectory optimization problem can be formulated as an optimal control problem. To discrete the optimal control problem, a Legendre pseudospectral (PS) method is used. Because the lunar landing from the parking orbit consists of the three phases such as a de-orbit burn, a transfer orbit phase, and a powered descent phase, the lunar landing problem is a multi-phase problem. Thus, the PS knotting method is also used to solve the multi-phase problem. This thesis presents two kinds of the trajectory optimization for lunar landing. One is two-dimensional trajectory optimization in order to understand the basic characteristic of the lunar landing trajectory. The other is three-dimensional trajectory optimization to deal with more practical landing problems. The trajectory optimization problems, dealt with in this thesis, could be applied to design the more precise trajectory for lunar landing.