An image processing apparatus capable of storing as many number of image files as possible, while adding file names conforming to a file storage standard, and capable of making it easy for a user to browse the desired image file among a vast number of continuously photographed image files. When one or plural representative images are selected from among continuously photographed images, a control unit of a digital camera as the image processing apparatus stores the one or more selected representative images into a memory card after a file name conforming to the file storage standard is added to each representative image, and stores continuously photographed images other than the one or more representative images into the memory card after file names not conforming to the file storage standard are added to these images.