By gradual change in structural design methods from strength based to performance based methods, typical existing frames could not satisfy the criteria of latter methods and if structures are designed by applying all related criteria, it will be an uneconomical design. Main problem in typical frames is imbalance between stiffness and ductility. To prevent large drifts, structures should have sufficient lateral stiffness and in order to absorb earthquake energy they must have high ductility. The goal of this research is to study the seismic performance of rigid and semi-rigid steel frames and the effects of adding friction dampers to such structures. In this paper, semi-rigid connections are supposed to yield and dissipate energy like dampers. For this purpose, 5-story building frames are designed in four cases including bare moment frame, moment frame with friction damper, bare semi-rigid frame and semi-rigid frame with friction damper. Dynamic time-history analyses are carried out applying three earthquake records. By observing the results of numerical analyses of structures, one can find out that semi-rigid frame with friction damper have the best performance among studied frames. Obtained results show that using friction damper in the moment frame with semirigid connections compared to the case with rigid connections, maximum first story displacement and base shear decrease respectively 7 and 20%.