The velocity-dependent oil damper is widely used in engineering. However, researchers and engineers found that oil dampers were damaged beyond maximum stroke during earthquakes and could not be reset due to the excessive residual displacement. Aiming at these problems, the pneumatic spring-oil damper with variable stiffness is proposed. The force-deformation relationship of the damper is derived, and its hysteretic characteristics are analysed. By applying traditional and new dampers to the dynamic analysis of a plane steel frame structure, we verify that the new damper can eliminate those shortcomings of traditional dampers. Dynamic analyses are performed for the 10- and 20-story three-dimensional steel frame structures using 5 typical ground motions, where two structures are equipped with new dampers. The results show that, compared to the initial structures, the peak displacements of the steel structures with new dampers decrease by approximately 10–75%, the inter-story drift angles decrease by approximately 25–60%, and the inter-story shear forces decrease by approximately 20–60%. Through an energy analysis, it indicates that the new damper has good energy dissipation performance and can dissipate approximately 30–70% of the total input energy. A comparative study between the new damper and the traditional damper is carried out. Finally, a parametric analysis for the pneumatic spring component shows that the axial length, the inner diameter, and the initial pressure affect the structural dynamic demands; therefore, these parameters should be reasonably designed before engineering application. The new damper in this paper is a more stable, safe, and efficient energy absorber for building structures.