In this study, the effect of steel damper with vertical slits on chevron braced frames with the number of different stories is investigated and pushover and cyclic analyses are performed . To evaluate and compare the results, a parametric study is carried out on a steel damper with and without slit. Eight model frames such as a single-story in ordinary moment frame, braced frame, chevron braced frame with gusset plate, chevron braced frame equipped by a damper with vertical slits, chevron braced frame with silt damper and three-story chevron braced frame equipped by a damper with vertical slits, five-story chevron braced frame equipped by a damper with vertical slits, eight-story chevron braced frame equipped by damper with vertical slits are modeled and analyzed by finite element method in Abaqus software. The results showed that the braced frame equipped by a damper with vertical slits by its ductile behavior, dissipated a large amount of earthquake input energy and reduced the base shear. The hysteresis curves were stable and without any loss, indicating high energy absorption by chevron braced frame equipped by a damper with vertical slits. In all the chevron braced frame equipped by a damper with vertical slits, the plastic hinges are not formed in the members of structures, and the failure mechanism is concentrated in the damper. The damper with vertical slits reduced the elastic stiffness, secondary stiffness and carrying capacity, which in addition to controlling the drift of the structure, increased the energy absorption capability. The chevron braced frame equipped by a damper with vertical slits had more ductility than other specimens, and according to the results, damper with vertical slits had good seismic performance.