A belt drive device is currently applied to machine tools and continuously variable transmissions of automobiles． The belt drive with a toothed belt，transmits the power between gears，and it controls the rotation angle of the load side by a torque generated from a driving motor side．The purpose of this paper，is to develop the method to take the measure of the appropriate action with respect to factors deteriorating the control performance in the positioning control of the belt drive device．The backlash is considered as a factor．Accordingly，the positioning accuracy is deteriorated，which may cause the limit cycle and the steady-state error．In this paper，we propose a positioning control system design method for a belt drive device in which backlash and characteristic uncertainties exist simultaneously． The backlash is regarded as a disturbance， the model of the controlled object is represented by a linear system，the influence of the backlash is suppressed，and the state equation using the matrix polytope representation relating to the uncertain parameters，We design a control system that guarantees robust stability with respect to uncertain parameters based on the H∞control theory. Experiment shows that the effectiveness of the proposed method comparing with other control system design methods．