An image processing device which is capable of efficiently performing face-detection, red-eye detection, and/or image data correction including red-eye correction without waste when there are a plurality of chances of performing the image data correction including the red-eye correction on a single image. A printing apparatus acquires image data and information concerning a face detection process performed on the image data from an image pickup apparatus. A controller of the printing apparatus determines to cause the printing apparatus to perform a face detection process on the acquired image data, based on the acquired information. The information contains an information item concerning detection accuracy of the performed face detection process, and a face detection process with higher detection accuracy than the detection accuracy described in the information is determined as the face detection process to be performed by the printing apparatus.