Thanks to recent lunar exploration missions, high-resolution lunar surface observation data was obtained. In future lunar exploration, landing is being requested at a specific point having higher scientific interest than other areas. The SLIM project is demonstrating pinpoint landing technology, which entails a combination of “autonomous image-based high-precision navigation technology” and “autonomous guidance technology intended to generate a fuel-optimum landing trajectory.” This paper presents powered descending trajectory design in terms of trajectory optimization. As usually considered in general space mission development, an optimal solution in terms of minimum fuel consumption is the basis of investigation. This study addresses trajectory optimization considering specific objective functions derived from practical constraints regarding mission design, such as altitude, downrange length, and visibility from ground stations. In this paper, nominal trajectory design considering minimum fuel consumption is first presented, followed by parametric studies to identify the sensitivity to changes in initial conditions under which powered descending starts. Finally, trajectory optimization results with various types of objective functions are presented.