Focusing device, image pickup apparatus, and control method

A focusing device includes a driving unit that drives a focus lens, a control unit, and a storing unit. The control unit controls the driving unit to move the focus lens through a predetermined range, determines a state of focus based on a signal from an image pickup unit, the signal being acquired in association with movement of the focus lens through the predetermined range, and controls the driving unit so that an object's image is in focus. The storing unit stores a position of the focus lens in focus acquired by the control unit. The control unit calculates a datum point of the range of movement of the focus lens, on the basis of the position of the focus lens in the storing unit, and shifts the range of movement of the focus lens in response to the calculated datum point in a direction in which the object moves.