A gyrostabilizer system that counteracts the natural rolling motion of a small boat or vessel. The invention constitutes an improvement in prior art systems of this type in that the system weighs less because it has a much lighter rotor made of composite materials spinning at much higher speeds. The gyrostabilizer system includes a lightweight rotor spinning at very high speeds to attain a large angular momentum. The mass of the rotor is concentrated away from the spin axis of the rotor to maximize angular momentum while minimizing weight. The rotor is mounted in a frame that, in turn, is mounted on gimbals so that the frame can be rotated about an axis that is normal to the longitudinal roll axis of the vessel. When the rotor is rotated about the gimbals, a torque is created that opposes the torque created by the sea and reduces the rolling motion of the vessel. The rotor may be mounted in an evacuated chamber to reduce air drag. Rotation of the rotor frame around the gimbal axis is controlled by an active servo system using information provided by roll angular position and angular velocity sensors.