Micro-electromechanical systems (MEMS) based on two-dimensional optical scan system is one of the core parts in the new generation three-dimensional imaging lidar system, which is developing towards to direction of low-cost, miniaturization and high-definition. Because of the limited aperture and maximum scan angle of the MEMS off- the- shelf, which can scan along two axes in bi- direction with high frame frequency, the laser beam reflected off the MEMS needs scanning angle expender and beam expender. We discuss the restrictive relationship between the spot size of the scan beam which is expended by Keplerian telescope system and the scan angle, derives the relationship between scan angle and the beam expender ratio, proposes the structure of a scan and zoom beam expender system which is based on MEMS and Keplerian telescope for three-dimensional imaging lidar system, and then on this basis gives an eleven piece type scan and zoom beam expender optical system designed by the optical design software Zemax, the result of the Zemax simulation has been shown perfectly conformed to the theoretical calculation.