In the earthquake resistant design of a building, it is very important to consider the effect of bi-directional ground motion. On the other hand, it is well known that the building with eccentricity between the gravity center and the lateral stiffness center has a disadvantage in the earthquake resistant design. In this paper, inelastic earthquake response analyses of a 30 story R/C space frame with eccentricity are performed using bi- directional severe ground motion, in order to investigate the torsional behavior of the highrise building. And we present the effect of eccentricity and bi-directional input motion on torsional displacement, hinge occurrence of members, ductility factor of beams, stress of columns and so on.