In view of the problems that influence of viscoelasticity of conveyor belt on starting process is neglected in current research on driving and control of belt conveyor, and belt conveyor starting process cannot be simulated well, mechanical properties and viscoelastic model of the conveyor belt were analyzed and Voigt model was selected for modeling of conveyor belt. Simulink and AMESim co-simulation platform was used to establish model of the mechanical part and motor control part of the belt conveyor separately. Three-point driving and control system of long distance belt conveyor was designed according to principle of direct torque control and the idea of cooperative control. The system adopts master-slave control strategy, takes head driving motor as main driver and the rest as slave drivers to control output speed and torque of the three drivers at the head part, middle part and tail part of the belt conveyor, which enables the belt conveyor to start and run smoothly with the preset speed curve. The simulation results show that although load torque of the conveyor is constantly changing due to viscoelastic effect of conveyor belt and the change of acceleration of the conveyor, the three drivers at the head part, middle part and tail part of the belt conveyor can track the preset starting speed well, which indicates that the three-point driving and control system can control the start-up and operation of the belt conveyor well.