1. An autofocus camera having a face recognition function, comprising: a photographing optical system including a focusing lens group movable along an optical axis; an image pickup device; an autofocusing system which performs a focus search process in which said image pickup device is activated to capture an object image at each of a plurality of different positions of said focusing lens group in said optical axis direction while said focusing lens group is moved along said optical axis to detect a position of said focusing lens group in said optical axis direction as an in-focus position based on said object images obtained at said plurality of different positions of said focusing lens group in at least one focus detection area, and further performs a focusing operation in which said focusing lens group is moved to said in-focus position that is detected by said focus search process; a switch which activates said autofocusing system upon being turned ON; a face recognition device for recognizing a face image based on said object images; and a controller which makes said autofocusing system set said focus detection area on a face recognition area at which said face image is recognized by said face recognition device and makes said autofocusing system perform said focus search process and said focusing operation on said focus detection area regardless of whether said switch is turned ON when said face recognition device recognizes said face image.