The structure of vertical axis wind turbine with wind speed-adapting is based on Darrieus straight-bladed turbine. It features that its blades are composed of movable and fixed blades. Through the opening and closing of the movable blades to adapt to the wind speed automatically, the turbine not only can start up in low wind speed, but also realize the conversion from drag-mode to lift-mode. Due to the special structure, the aerodynamic model of this turbine in drag-mode is different from that of Savonius and Darrieus turbine. So in this article, the aerodynamic model of this turbine in drag-mode is established. Then the coefficient of start-up torque is calculated and compared with that of Darrieus straight-bladed turbine which has the same size. The results show that the start-up performance of this turbine is obviously better than that of Darrieus straight-bladed turbine.