In this paper, analysis of variance on designed experiments with full factorial design was applied to determine the optimized machining parameters for ultra-precision fabrication of the secondary aspheric mirror, which is one of the key elements of the space cryogenic infrared optics. A single point diamond turning machine (SPDTM, Nanotech 4μpL; Moore) was adopted to fabricate the material, AL6061-T6, and the three machining parameters of cutting speed, feed rate and depth of cut were selected. With several randomly assigned experimental conditions, surface roughness of each condition was measured by a non-contact optical profiler (NT2000; Vecco). As a result of analysis using Minitab, the optimum cutting condition was determined as following; cutting speed: 122 m/min, feed rate: 3 mm/min and depth of cut: 1 μm. Finally, a 120 mm diameter aspheric secondary mirror was attached to a particularly designed jig by using mixture of paraffin and wax and successfully fabricated under the optimum machining parameters. The profile of machined surface was measured by a high-accuracy 3-D profilometer(UA3P; Panasonic) and we obtained the geometrical errors of 30.6 nm(RMS) and 262.4 nm(PV), which satisfy the requirements of the space cryogenic infrared optics.