1. An apparatus for correcting brightness of a moving image, comprising: a face image detecting device for detecting a face-image portion from within one subject image constituting a number of frames of subject images applied in succession one frame at a time at a fixed period; a still-image brightness correction parameter calculating device for calculating a still-image brightness correction parameter based upon brightness of the face-image portion detected by said face image detecting device; an adjustment parameter calculating device for calculating an adjustment parameter, which adjusts the still-image brightness correction parameter calculated by said still-image brightness correction parameter calculating device, based upon another subject image preceding the one subject image; a moving-image brightness correction parameter calculating device for calculating a moving-image brightness correction parameter by adjusting the still-image brightness correction parameter, which has been calculated by said still-image brightness correction parameter, using the adjustment parameter calculated by said adjustment parameter calculating device; and a brightness correcting device for correcting the brightness of a correction-target subject image, which is subsequent to the one subject image, using the moving-image brightness correction parameter calculated by said moving-image brightness correction parameter calculating device.