This manuscript presents a comparative study between the seismic collapse performances of steel moment-resisting frames (MRFs) with the same additional damping ratio while equipped with linear and nonlinear viscous dampers. Three steel moment-resisting frames of 6, 8 and 12 stories were designed based on ASCE 7–10 with and without dampers. The characteristics of the linear (α = 1) and nonlinear (α = 0.5) dampers were then assigned while assuming equal damping ratios (20% for the models of 6 and 8 stories, and 25% for the model of 12 stories). The sophisticated nonlinear model of the structures was then developed in Opensees considering both cyclic strength and stiffness deterioration with lumped plasticity as well as the linear and nonlinear dashpot for dampers while nonlinear geometry was included in all the models. The collapse probability was calculated using well-known incremental dynamic analysis (IDA) under far-field records. The paper demonstrates that the use of damper improves the performance of the steel MRFs and reduces the collapse probability in comparison with the conventional steel MRFs. Moreover, it was observed that steel MRFs with linear dampers have better collapse performance than steel MRFs with nonlinear dampers for the same damping ratio.