The facade of one high rise building is designed as Pipa tower, which used steel-concrete composite structure. The middle part of Pipa tower is concrete shear wall tube, and around columns are steel columns with box-section. The height width ratio of this bulding is severe out-of-codes. By means of ANSYS program two kinds of dynamic stabilities excited by earthquake of this building are studied by the method of time history response analysis. The first definition of dynamic stability is essentially dynamic buckling based on the definition of Lyapunov, which is analyzed by a modified time freezing method and dynamic eigenvalue method; the second one is the problem of dynamic ultimate load carrying capacity, which is obtained by combing Incremental Dynamic Analysis (IDA) with Budiansky & Roth (B-R) criteria. Results show that this building is of a poor performance of dynamic stability, some parts must be reinforced. Therefore, the presented method can supply a reliable and feasible computing approach for the stability analysis of such super tall and complex buildings.