A vibration suppressing structure including a main structure and a vibration suppressing section disposed in an upper portion of the main structure which is provided with an auxiliary structure adapted to undergo vibration in response to the vibration of the main structure occurring due to a disturbance, an auxiliary mass, a driving device, and a damper. The displacement of the auxiliary structure caused by the vibration is transmitted to the auxiliary mass via the driving device, and the auxiliary mass is controlled by an amount of movement directly proportional to the amount of displacement. The vibration suppressing section is arranged such that the damping coefficient of the damper, the magnitude of the auxiliary mass, and the ratio of the amount of movement of the auxiliary mass to an amount of displacement of the auxiliary structure which are included in a mass matrix M T for the vibration suppressing section, a damping matrix C T , a stiffness matrix K T , a location vector i T of a disturbance, are adjusted in such a manner that the relationships of (ω T j ) 2 ·M T ·i T =K T ·i T and 2h T ·ω T j ·M T ·i T =C T ·i T hold, with respect to a natural frequency ω T j of a j-th mode and a predetermined damping factor h T , thereby constituting a system of a pseudo singe degree of freedom. A vibration suppressing structure is obtained which is capable of effectively suppressing vibrations in a multi-storied structure and which can make effective use of the space within the structure.