In X-ray computed tomography (CT) the real rotation axis position often does not coincide with the assumed one: technical imperfections of the tomographic setup, the fast speed of movement of the gantry and goniometer cause rotation axis displacements and inclinations. At the same time the use of incorrect axis location parameters during reconstruction leads to the appearance of so-called tuning-fork artifacts in the form of stripes and blurs at the object boundary. The existing rotation axis alignment methods for cone-beam CT require a large amount of computing resources, are laborious in implementation, are not able to accurately determine several axis location parameters at once, or are based on the processing of additional equipped with reference markers object post-scans and shots that are not always available. Thus the rotation axis alignment methods development in the cone-beam CT still seems to be relevant. In this paper, the developed model for parameterizing the rotation axis position is described and justified. The novel several-stage automatic method for rotation axis parameters determination is described. The proposed method is based on usage of mean projection image and tested both on synthetic and real data in parallel-beam and cone-beam geometric schemes. The absolute error of that method on the simulated data is no more than 1 pixel and 1 degree, respectively for shift and slope.