1. An X-ray CT apparatus comprising: an X-ray source provided with an X-ray tube for irradiating X-rays and an X-ray tube control device for controlling the X-ray tube; an X-ray detector arranged facing the X-ray source having an object therebetween, for detecting the X-ray and outputting X-ray projection data; rotation means to which the X-ray source and the X-ray detector are mounted and is capable of rotating them; image processing means for reconstructing a tomographic image based on the X-ray projection data; input means for inputting an image quality index value which indicates a desired index of image quality with respect to the tomographic image obtained by the image processing means; model generation means for generating an object cross-sectional model in the body axis direction of the object from a scanogram data of the object; optimization means for setting an irradiation modulation curve indicating a desired optimum X-ray irradiation dose based on the object cross-sectional model and the image quality index value, and modulating the X-ray irradiation dose based on the set irradiation modulation curve; image quality estimation means for estimating the image quality of the supposed image using optimization by the optimization means when rotation scanning is performed by modulating the X-ray irradiation dose based on the irradiation modulation curve and the image quality of the supposed image without using optimization by the optimization means when the rotation imaging is performed without modulating the X-ray irradiation dose based on the irradiation dose modulation curve; and display means for displaying the image estimation result of the image estimation means.