Ion beam figuring is suitable for the final correction of the surface figure error of aspherical substrates in an extreme ultraviolet lithography optics. This paper reports the investigation of the surface roughness of ULE® substrate machined by an Ar+ ion beam of 3–10keV. For an Ar+ ion beam in the range of 3–10keV, the mid-spatial frequency roughness of the surfaces machined to a depth of 50nm was comparable to the surface roughness of an unprocessed one. The high-spatial frequency roughness of the unprocessed surface was 0.08nm rms; whereas, the HSFRs of the surface of the substrate at Ar+ ion beam of 3, 5, 7, and 10keV were 0.10, 0.14, 0.16, and 0.17nm rms, respectively.