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 an optical axis direction while said focusing lens group is moved along said optical axis to detect a position of said focusing lens group in the optical axis direction as an in-focus position based on 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; an autofocus switch which activates said autofocusing system upon said autofocus switch being turned ON; a face recognition device for recognizing a face image based on the object images; and a controller which controls said autofocusing system to set said focus at said at least one detection area on a face recognition area at which said face image is recognized by said face recognition device and controls said autofocusing system to perform said focus search process and said focusing operation on said at least one focus detection area regardless of whether said autofocus switch is turned ON, upon one of a lapse of a predetermined period of time after said face recognition device recognizes said face image and said face recognition device consecutively recognizes said face image a predetermined number of times, when said face recognition device recognizes said face image.