The present invention proposes a single-axis-control-input gyroscope system having imperfection compensation, which comprises a gyroscope and a state observer. The gyroscope includes a mechanical structure, and the dynamic behavior of the mechanical structure is described with a plurality of system parameters and a plurality of dynamic equations. The system parameters include a mass of the gyroscope, two main-axis spring constants, a cross-axis spring constant, two main-axis damping coefficients, a cross-axis damping coefficient and an angular velocity. The mechanical imperfections cause the system parameters to deviate from the designed values and become unknown values. The gyroscope receives a single-axis control signal and outputs a plurality of gyroscopic system dynamics. The single-axis control signal includes at least two frequency signals. The state observer is coupled to the gyroscope to receive the gyroscopic system dynamics as the inputs thereof to feed back compensations to the state observer. Thereby is estimated an angular velocity.