This paper presents a parameter varying control of a magnetorheological (MR) damper with stiction effect and its application to seismic protection of a model two-story structure. This semi-active device is utilized to reduce the vibrations of the model structure due to earthquake excitations. A modified Bingham model is used to capture the nonlinear hysteretic dynamics of the MR damper including the stiction effect. The parameters of the model are identified by solving a nonlinear optimization problem. The Bingham model is considered because of its simple structure to be used in linear parameter varying (LPV) controller design. The model is verified experimentally showing an acceptable level of accuracy. The second part of the paper addresses the LPV controller design to command the MR damper to suppress the structural vibrations. The LPV controller is designed for the combined structure and MR damper based on the Bingham model. The scheduling parameter is chosen to be damper velocity which is obtained by measurement. An optimal passive damping design is also obtained for comparison purposes. The performance of the controller is compared with the optimal passive damping case for El Centro and Northridge earthquakes with different intensities. The experimental results show the improved performance of the LPV controller design approach in terms of the maximum acceleration and the RMS values of the structure response.