An X-ray imaging apparatus includes an X-ray generator configured to transmit X-rays to an object, an X-ray detector configured to detect the X-rays transmitted through the object and convert the detected X-rays into electrical signals, a gantry in which the X-ray generator and the X-ray detector are installed so as to be opposite to each other, the gantry being rotatable about a bore, a controller configured to control a rotation of the gantry during bio-signal cycles of the object so that the gantry is rotated from different start positions whenever one of the bio-signal cycles is started, and an image processor configured to generate a 4D image of the object by applying a prior image-based compressed sensing image reconstruction algorithm to plural 2D projection images acquired from the electrical signals generated by converting the X-rays detected during the rotation of the gantry.