The Vector Form Intrinsic Finite Element (VFIFE) method was recently proposed for structural behavior analysis based on vector mechanics. It presents great advantages over other analytical methods, especially in the complicated behavior analysis of structures. In this work, viscous damping elements were developed based on VFIFE theory and dynamic analysis of the resisting vertical progressive collapse of a plane steel-frame structure with viscous dampers was performed. A transient unloading method program was developed to realize the unity of static and dynamic analysis before and after component removal. The performance requirements of damper arrangement and parameters during vertical progressive collapse were studied, and the progressive collapse resistance for framed structures with and without viscous dampers were compared considering the vertical displacement curves of failure point, beam-end angles, dynamic magnification factor, and the plastic hinge distribution of the structure as references. The analysis results show that VFIFE is an effective method for studying the dynamic response of vertical progressive collapse of structures and that reasonable arrangement of dampers can effectively control the deformation and vibration of structures, reduce the internal force of the components, reduce the number of plastic hinges, and greatly improve the progressive collapse resistance of structures.