The present invention generally refers to computed tomography (CT) based imaging systems and, more particularly, to a fast 3D tomosynthesis scanner apparatus and CT-based method without focal spot motion during continuous tube movement around an object of interest (O) or tissue region (M) to be examined (herein also referred to as “object”), which may advantageously be used in cone-beam volume CT mammography imaging so as to avoid motion artifacts and blurring effects. According to the present invention, said 3D tomosynthesis scanner apparatus is adapted to perform a rotational step-and-shoot image acquisition procedure for acquiring a set of 2D projection images during a continuous rotational movement of an X-ray tube (101) in an azi-muthal direction (+φ) along an arc segment of a circular trajectory when rotating around said object (O, M) and subjecting these 2D projection images to a 3D reconstruction procedure. According to the present invention, it is foreseen that, during the image acquisition time for each 2D projection image, the focal spot on the X-ray tube's anode is moved in an opposite direction (−φ)from a start position (bs) to an end position (be) with respect to the rotary X-ray tube's housing such that the azimuthal path distance (Ab) covered by the X-ray tube (101) due to the continuous rotational tube movement during this time is compensated. The 3D tomosynthesis scanner further comprises a mechanism for switching the focal spot on the X-ray tube's anode back to its start position (bs) with respect to said tube housing before starting a new image acquisition process for acquiring image data of a next 2D projection image. The superposition of the focal spot movement with respect to the tube housing and the continuous rotational movement of the X-ray tube (101) along said arc segment results in a stationary focal spot position relative to the object (O, M) and a stationary X-ray detector (104) diametrically oppositely arranged to the X-ray tube (101) with respect to said object (O) for each of the individual 2D projection images.