The invention provides a Fourier expansion based gyro stabilizer and a realization method thereof, relates to the technical field of robot control, and aims at solving the control difficulty caused by narrow angle range of procession force torque of gyros and non-linear relation between the procession force torque and procession force angle when a dual-gyro stabilizer is used to maintain stable attitude of a single-wheel robot. The gyro stabilizer comprises a lower connecting piece, an upper connecting piece and two groups of gyros, each group is composed of multiple gyros, self rotation of each gyro is driven by an independent motor, in each group, procession of the gyro at a middle position is driven by a procession motor, and procession of gyros in the surrounding is transmitted by groups of synchronous pulleys of fixed transmission ratio. The stabilizer and realization method are used for attitude stabilization of single-wheel robot system as well as attitude adjustment of small aircrafts and satellites.