For accurate reflection wavefront error correction of imaging soft X-ray multilayer mirrors, a period-by-period ion milling system was developed. A stable and homogenized radial distribution of ion beam was realized for an ion milling over a whole area of 100 mm-wide multilayer. To demonstrate the wavefront error correction principle, a dielectric multilayer mirror for visible light was locally milled by our system. Wavefront as measured by a phase shifting interferometer showed the reflection phase of local milling multilayer advanced. Area-selected ion millings with mask templates made of Mo and Si, and by photoresist contact masks were carried out. Although striped patterns generated by the difference of spectroscopic reflectance between Mo and Si were observed at peripherals of milling area when templates were used, a clear and sharp edge pattern was obtained with contact mask. Soft X-ray reflectance of a Mo/Si multilayer milled with photoresist contact mask showed good feasibility of precise wavefront error correction of multilayers. These results proved our phase correction method is promising and practical for the 0.1 nm-period correction of soft X-ray multilayer mirror.