Aimed at the solution of the contact problem in the involute cylindrical worm and the helical gear transmission pair, a mathematical model of conjugate tooth surface contact geometry of the involute cylindrical worm and the helical gear was established based on the gear geometry theory and the differential geometry. Taking a transmission pair equipped in a type of horizon drive machine as an example, we simulated the tooth surface contact of the worm helical gear transmission pair with numerical analysis and carried out the experiment of tooth surface contact. The analysis results show that the contact position and contact area can be effectively controlled by adjusting the transmission parameters such as transmission ratio, normal pressure angle, normal modulus and helix angle and they will have a theoretical significance for the design and manufacture of the cylindrical worm and the helical gear transmission pair.