This paper presents a new recirculating roller screw mechanism. The new recirculating roller screw mechanism consists of multi-thread screw, outer ring roller, multi-thread nut, carrier, roller circulation control parts and other parts. Based on the structural characteristics of the new recirculating roller screw mechanism, the thread surface equations of the screw, roller and nut are derived. The meshing equations for calculating the contact position at the screw-roller and the nut-roller interface are established. Through the principle of differential geometry, the thread surface equations of the meshing parts of the recirculating roller screw mechanism are established, and the meshing equations at the screw-roller and the nut-roller interface are derived. The influence of structural parameters on the contact position and axial clearance between threads is analyzed. The results show that under the influences of number of starts, nominal radius and flank angle, the contact positions of each pair of meshing thread teeth are constantly changing. The larger nominal radius of the screw and the smaller number of starts are beneficial to the contact point close to the middle diameter tangent point at the screw-roller interface. The contact position at the screw-roller interface is very sensitive to the difference of the flank angle of the two parts. When the flank angles of the screw and the roller are the same, the contact point is located near the tangent point of nominal circles of the two parts.