The building-damper system designed by a seismic code is usually considered to be able to withstand the attack of strong earthquakes. However, near-fault earthquakes, especially those with the forward-directivity effect, might cause early and unexpected failure of code-designed dampers and consequent severe structural damage. In this paper, by taking into account near-fault earthquakes, seismic performance of the building-damper system and damper failure’s influence are evaluated systematically. A 9-storey steel building is designed by the Chinese seismic code as the benchmark model, and five typical dampers, including buckling-restrained brace damper (BRB), friction damper (FD), self-centering damper (SCD), viscous damper (VD), and viscoelastic damper (VED), are adopted. It was found that the building-damper systems show a large response and possible damper failure under the near-fault earthquake excitations. Then, the influence of damper failure is investigated, which reveals that damper failure would significantly affect seismic performance of the building-damper system, especially for the building-SCD system. Subsequently, by introducing the artificial near-fault earthquake excitation, the influences of different pulse parameters, such as pulse velocity amplitude, pulse period, and the number of significant pulses, are studied. It shows that the pulse velocity amplitude and pulse period obviously affect the seismic performance, while the number of significant pulses presents little influence.