Space optical communications terminals frequently rely on optical telescopes to enhance the transmitted and received efficiency of the communication system. An optical design of a space laser communications optical antenna system was proposed to overcome the traditional on-axis Cassegrain optical antenna′s disadvantages of small field of view and low emission efficiency. As an example, an optical antenna system operating at 0.85 μm, 1.064 μm and 1.55 μm with aperture size 150 mm, magnification 15 was designed. The initial parameters were computed, and the ray tracing and optimization for the optical antenna system were performed with ZEMAX-EE software. The analysis results demonstrate that the Root Mean square(RMS) of a spot radius is less than 10 μrad in the working wavelength(0.85 μm, 1.064 μm, 1.55 μm), which implements astigmatism correction and obtains a good diffraction-limited quality in a wide spectral region and a high magnification. These results prove the feasibility of the optical design method proposed.