In this paper, the periodic semicircle groove disk is investigated to restrain the multipactor phenomenon in high power pill-box window. Through the theoretical analysis, the semicircle groove is proved to avoid the local field enhancement, which always exists in the vicinity of the sharp boundary groove. The proper groove width with a corresponding minimal suppression tangential electric field is achieved by simulating the multipactor procedure with Monte-Carlo algorithm. The effect of normal electric field is also analyzed. This configuration is to be applied to the high power klystron.