In this paper, we developed modeling of tension and speed dynamics for a two-drum winder in a three span continuous web transport system which had not been previously. Dynamic modeling of the time-varying nonlinear system was derived by considering the effect of the radii and mass moment of inertia in the unwinder and the two-drum winder through winding up the web. After linearizing it, we designed with a variable-gain a PID controller for tension control and a PI controller for speed. Simulation is carried out with the variation of radii and moment of inertia at high speed for the proposed tension control system with the two-drum winder and the variavle-gain a PID controller. Results show good performance of tension control during the speed change speed at a start-up and stop.