When the high-contact-performance cylindrical gear serving as a driving gear and the high-contact-performance cylindrical gear serving as a driven gear are in meshing transmission, the relative curvature kr meets the condition that kr = k1-k2 = ar2 + br + c, r is the distance from a meshing point C to a node P, k1, k2, k3, k4, k5, k6, k7, k8, k7, k8, k8, k8, k8, k8, k8, k8, k8, k8, k8, k8, k8, k8, k8, k1, k2 are respectively curvatures of the tooth profile sigma 1 of the driving gear and the tooth profile sigma 2 of the driven gear at any meshing point C, and a, b and c are coefficients of a quadratic polynomial. Compared with the prior art, the cylindrical gear with the high contact performance can obtain higher contact, bending, abrasion and gluing bearing capacity and better lubricating performance.