A research has been carried out on the influence of structural eccentricity and velocity pulse earthquake on the seismic response of the new gravity column-core tube structure. With three velocity pulses along with three corresponding non-velocity pulse seismic records selected as the ground motion input, and by using CANNY software, a nonlinear dynamic time history analysis of eccentric gravity column core tube structure has been made to study the influence of velocity pulse effect and eccentricity on elastic-plastic seismic response. The results show that the inter-story shear force, inter-story displacement, inter-story torque and inter-story torsion angle of the structure are greatly higher than those under velocity pulse earthquake, with the eccentricity exerting great effect on the elasto-plastic seismic criteria of the structure. Specifically, the vertex displacement, inter-story displacement angle, inter-story torque and inter-story torsion angle increase positively with the increase of eccentricity, while the inter-story shear shows a decreasing trend. Therefore, it is suggested that the effects of velocity pulse earthquake and eccentricity should be taken into consideration in the design of new gravity column core tube structure.