The traction drive continuously variable transmission is another kind of advanced transmission device for vehicle beside the metal pushing V_belt type CVT. It provides excellent driving performances including powerful driving capacity, high efficiency, good smoothness and economy, etc. The basic structure, transmission principle and the hydraulic servo control system of traction drive CVT are described. The mathematical model of the system is established. The study of this project provides the academic bases of further studying on the dynamic characteristics of CVT and vehicle.