Abstract: Using reaction wheels to control the attitude and thrusters for station-keeping, the satellite's inertial may be changed. A vector observation algorithm based on kinematics applied to the gyro fault diagnosis is presented in the paper. Using the Generalized Rodrigues Parameters (GRPs) to describe the satellite's attitude may avoid that the mode of quaternion is not equal to one. Using quaternion to compute the satellite's kinematics can also avoid the GRPs' complex integral. Both small change and slow decrease of angular velocity range is simulated when gyro's rapid and slow change faults occur. The result shows that the algorithm can estimate body's angular velocity effectively and diagnose the gyro fault accurately under the two situations above. The algorithm is not affected by body's inertial and control torque with a smaller amount of calculation, and have a potential value to the engineering application.