The X-ray CT apparatus of the embodiment includes an X-ray generating part, an X-ray detector, a reconstruction function setting part, and a reconstruction processor. The X-ray generating part generates X-rays while rotating in a circuital orbit around the subject. The X-ray detector has a plurality of channels and detects the X-rays transmitted through the subject in each channel. The reconstruction function setting part sets the reconstruction function using statistics representing the statistical dispersion of the X-ray amount of the detected X-rays and a predetermined reference reconstruction function. The reconstruction processor carries out the reconstructing the projection data based on the detected X-rays based on the reconstruction function and produces image data.