Abstract: A new laser beam expander with magnification of 40× as well as on-axis and off-axis aberration corrected properly, was designed based on the third-order aberration theory. This system is realized by two-step beam expanding based on a simple Galilean structure. The beam path of the system is folded by four lenses, two second-order aspheric surfaces and two mirrors (or a prism). The optical mechanical parameters, outline drawing and image evaluation are given by the aid of optical design software CODE V. This system features simple design and structure, low cost, high image quality and good performance.