An X-ray computed tomography (=CT) apparatus (10), comprising- an X-ray source (11) for emitting an X-ray beam (1), in particular a divergent X-ray beam (1), along a beam axis (z),- a filter element (2) for attenuating the X-ray beam (1),- a stage (14) for an object (3) to be investigated with the attenuated X-ray beam (1a),- a 2D X-ray detector (15) with a detection area (15a),- and a gantry system (16) capable of rotating either the entirety of the X-ray source (11), the filter element (2) and the 2D X-ray detector (15), or the stage (14) for the object (3) with respect to a rotation axis (x) which is perpendicular to the beam axis (z),wherein the filter element (2) has a spatially varying X-ray absorption capability along a cross direction (y) which is perpendicular to both the beam axis (z) and the rotation axis (x),is characterized in that the spatially varying X-ray absorption capability exhibits a maximum absorption along the cross direction (y) at a zero position (y0), wherein X-rays passing through the filter element (2) at the zero position (y0) intersect the rotation axis (x). The invention provides a CT apparatus which allows to further reduce the radiation dose for an object to be investigated, while retaining a high image quality at the same time.