Limitation in building design due to high wind velocities is always a prime problem for engineers. Prime concern is safety for skyscrapers while maintaining architectural identity. The factors like wind currents and earthquakes make it difficult for designing high rise buildings. Various kind of vibrations are created in upper region of buildings subjected to higher wind load. Various methods are adopted to damp these vibrations, for example Tuned Mass Dampers are used in Taipei 101 in upper floors to damp wind vibrations. These methods have limitation for higher cost and lower range for vibrations. Additional design need to be provided to make a self-damping system. Our proposed idea is to create an advanced self-stabilizing Gyroscopic Damping system that could be flexible and scalable for any wind load and vibration at any height. The system would be a set of giant gyroscopes tuned to provide an excess inertia to the top floors against wind, concept of angular momentum is adopted to redirect the moment created by wind load to a safe vertical axis.