1. A digital image processing apparatus for blurring an image background comprising: an optical portion that receives light reflected from an object and includes an auto-focus lens; an auto-focus motor that moves the auto-focus lens; an imaging portion that converts the light to at least one of a moving image and a still image; a digital signal processing unit for comparing focal distances of frames of the moving image with a focal distance of the still image, applying background blurring to the still image according to differences between the moving image focal distances and the still image focal distance, and controlling the auto-focus motor to move the auto-focus lens from a home position to an infinite position during capturing of the moving image, the digital signal processing unit comprising: a focal distance calculation unit detecting the focal distances from the frames of the moving image; a comparison unit comparing the focal distances of the frames with the focal distance of the still image; and a control unit controlling background blurring to be applied to a predetermined portion of the still image in which a focal distance of the still image is different from focal distances of the frames.