During an earthquake, yielding dampers yield before the main members of the structure and with their plastic deformations, they dissipate part of the earthquake energy. Therefore, ductile materials are a suitable option for this type of dampers. In this research, numerical studies were conducted to investigate the effect of aluminum yielding damper (AYD) on semi-rigid steel frame. First, the steel frame and the AYD were verified based on experimental samples and analytical equations. An approximate equation for estimating the elastic stiffness of the damper was also presented. Parametric studies were conducted in order to investigate the effect of the number of dampers and the axial force of the column on the stiffness, ultimate strength, ductility and energy dissipation parameters of the frame. The additional forces applied to the connections, beams and columns of the frame due to the addition of dampers were also calculated, which is important in the design of the frame. The results showed that the addition of the damper increased the frame's stiffness, energy dissipation, ultimate strength, and ductility, and also reduced the negative effect of the column's axial force on energy dissipation of the frame.