The structure analyzed in this paper has particular building style and special structural system. It is a rigid-connected twin-tower skyscraper with asymmetrical distribution of stiffness and masses in two towers. Because of the different stiffness between the north and the south towers, the torsion seismic vibration is significant. In this paper, in order to study the seismic response of the structure under both frequent low-intensity earthquakes as well as rare earthquakes at the levels of intensity 7, the analysis model is built and analyzed with NosaCAD. NosaCAD is an nonlinear structure analysis software based on second-development of AutoCAD with ObjectARX. It has convenient modeling function, high computational efficiency and diversity post-processing functions. The deformations, forces and damages of the structure are investigated based on the analysis. According to the analysis, there is no damage on the structure under frequent earthquakes, and the structure has sufficient capacity and ductility to resist rare earthquakes. Therefore the structure can reach the goal of no damage under frequent earthquakes and no collapse under rare earthquakes. The deformation of the structure is below the limit in Chinese code. The time sequence and distribution of damages on tubes are reasonable, which can dissipate some dynamic energy. At last, according to forces, load-carrying capacity and damage of elements, there are some suggestions on increasing the reinforcement in the core tube at base and in stiffened stories.