This paper optimizes the thread profile of the planetary roller screw mechanism to improve the bearing capacity of the planetary roller screw mechanism. A meshing method based on convex-concave contact is proposed and the thread profile of screw and nut with a concave arc is designed. Based on the space meshing theory, the thread surface equation and the space meshing equation are derived, and the load distribution model is established based on the Hertz contact theory and the deformation coordination equation. The contact point position, the axial clearance and the contact stress are calculated by the numerical calculation method, and the law of the flank angle, pitch and other parameters on the contact point position, the axial clearance and the load distribution are revealed systematically. The contact stress between the standard and the convex-concave contact planetary roller screw mechanism is compared. The results show that the flank angle has the greatest influence on the axial clearance. The changes of the concave arc radius of the screw and nut make little difference to the contact point position and the axial clearance, but have a great impact on the bearing capacity. The bearing capacity of the convex-concave contact planetary roller screw mechanism is greatly improved compared with the planetary roller screw mechanism. The smaller the concave arc radius of the screw and nut, the more obvious the improvement of the bearing capacity. This research provides a basis for optimal design and analysis for the development of the planetary roller screw mechanism with high load capacity and long service life.