The elastoplastic response of a new type of gravity column core tube structure system was studied by considering comprehensive adversary conditions of pulse like ground motion and structural mass eccentricity. Ten pulse like and ten non pulse like ground motion acceleration records were selected as bidirectional seismic input. The structural nonlinear analysis software CANNY was used to conduct a finite element numerical analysis, and the effects of pulse like ground motion and structural mass eccentricity on the elastoplastic seismic response of the new structure were investigated. The analysis results indicate that the story drift ratio, shear force, and inter story torsion angle under pulse like ground motions are remarkably higher than those under non pulse like ground motions. Besides, mass eccentricity apparently affects the elastic plastic seismic demand of the structure. With the increase in eccentricity, the story drift ratio and inter story torsion angle increase while the inter story shear decreases. It is recommended that attention should be paid to coupling adversary influence of pulse like ground motion and structural mass eccentricity during the design of the gravity column core tube structure.