Aiming at the problems such as unsatisfactory actual meshing effect and unreasonable distribution of contact spots of the cylindrical worm transmission pair in the grader rotary drive, the mathematical model of the transmission pair was established and its meshing characteristics were studied. An accurate 3D solid model was established, and the contact characteristics of the transmission pair were analyzed by contact finite element method, which verified by using numerical examples and sample tests. The results show that the undercutting can be effectively avoided by selecting proper displacement coefficient; the maximum stress of the tooth surface can be reduced by reasonable increasing the diameter of the worm gear hob, modifying the driving pair and properly rounding the worm root and the worm gear root;the contact spots detection results of the transmission pair are consistent with the contact finite element analysis results, which proves the validity of the analysis method; the transmission efficiency of the improved worm reducer is between 38% and 43%, and the transmission efficiency during forward rotation is slightly higher than that during reverse rotation.