1. An X-ray CT apparatus comprising: an X-ray source configured to irradiate X-rays to an object to be examined; an X-ray detector disposed facing the X-ray source, configured to detect the X-rays which are transmitted through the object; a scanner in which the X-ray source and the X-ray detector are mounted, configured to rotate them around the object; an image reconstruction device configured to reconstruct a tomographic image in an imaging region of the object based on the transmitted X-ray dose from a plurality of directions detected by the X-ray detector; and an image display device configured to display the reconstructed tomographic image, characterized in further comprising: an elliptic model generating function configured to generate an elliptic model including a circle, which is approximated to the cross section of an imaging region of the object and has an X-ray attenuation coefficient which is effectively equivalent to that of water, based on the maximum height and the area of the projection value profile of the imaging region of the object which is acquired by scanogram imaging; an elliptic model adequacy determining function configured to determine whether an elliptic model is adequate for the model of an imaging region or not; a corrected elliptic model generating function configured to generate a corrected elliptic model based on the amount of characteristic of the projection value profile in the case that the elliptic model is determined to be inadequate for the model of the imaging region by the elliptic model adequacy determining function; and a radiation dose controlling function configured to control the X-ray dose to be irradiated from the X-ray source based on the elliptic model or the corrected elliptic model.