In the fiber optic gyroscope (FOG) single-axis rotation inertial navigation system (SRINS), the -axis gyro drift () dramatically limits its navigation precision and the -axis gyro scale factor error () can cause greater navigation error because of the rotation process compared with the strap-down inertial navigation system. Hence, identification and compensation for the and are important in SRINS. An approach based on the azimuth error model of open-loop algorithm is proposed. This approach considers azimuth angle as a measurement and uses a least recursive square algorithm for identifying the and . Compared with the traditional method, which takes velocity and position errors as measurements, the time required for identifying with the proposed method is only approximately 10 min, while the traditional method requires 6 h to 12 h. Experimental results from an SRINS with FOGs demonstrate that the accuracy of identifying the reaches 0.002°/h and that of the reaches 8 ppm in 10 min. The positioning accuracy of the SRINS improves greatly after the identification and compensation.