A research has been conducted on the influence of velocity pulse type seismic actions on the elastic-plastic structural seismic response, taking into consideration the dual adverse conditions of pulse-ground motions with a vertical irregularity. Based on the design of a new type of 20- and 30-story typical gravity column core tube structure, a series of vertical irregular structures can be obtained by changing the stiffness of the bottom story. With 10 velocity pulse and 10 non-velocity pulse seismic records selected respectively, an elastic-plastic dynamic time history analysis is conducted on the vertical irregular gravity column core tube structure by using CANNY software, with a further study on the influence of velocity pulse effect and vertical irregularity on the elastic-plastic seismic response of the structure. The results show that the inter-story shear force, inter-story displacement and overturning moment of the structure under velocity pulse-like ground motions are significantly higher than those under non-velocity pulse-like ground motions. The vertical irregularity has a significant impact on the structural elastic-plastic seismic demand. The inter-story displacement angle increases with a decreasing vertical irregularity ratio, while the inter-story shear force and overturning moment show a slightly decreasing trend. It is suggested that the coupling effects of velocity pulse-like motions and the vertical irregularity should be considered in the design of new gravity column core tube structures.