1. An auto-focus apparatus utilized for an image pickup apparatus having a focus ring comprising: an evaluation value calculator periodically calculating a plurality of evaluation values for a plurality of areas of a subject image based on high frequency components of image signals of the plurality of areas of the subject image; and a control unit, after detecting that the focus ring has been stopped, performing image processing on an area of the subject image where fluctuations of the evaluation values obtained just before the focus ring has been stopped exhibit a predetermined history, based on an evaluation value obtained in the area of the subject image exhibiting the predetermined history, and outputting instruction signals for moving a focus lens base on a peak of the evaluation values obtained by the image processing.