The installation error of the star sensor was one of the main factors restricting the accuracy of SINS/CNS navigation. It was necessary to calibrate it before use, especially the NFOV star sensor could not obtain the attitude information from a star map. This paper proposed a fast and high-precision calibration method for SINS/CNS integrated navigation system. The attitude and velocity output by the inertial navigation and the vector information measured by the star sensor were used to construct quantity measurements. A Kalman filter model was established to realize the ground calibration of installation error and inertial device constant error. Through global observability analysis, the observability of the system under different carrier attitudes and star points was given and verified. The simulation results show that the carrier needs to rotate in at least two axes and observe stars three times, and the star point should not be located at the star sensing measurement origin, so as to estimate the three-axis installation error of the star sensor with high precision. For a FLOV star sensor, part of the carrier attitude is not conducive to improve the observability of the system. The estimation accuracy of carrier attitude and star-sensitive installation errors is within 0.5″ and the constant errors of gyro and accelerometer are less than 0.000 7(°)/h and $0.3\;{\text{μg}}$, respectively. This method can achieve high-precision calibration without sophisticated external equipment and manual reference. It has certain significance for the stargazing scheme design of SINS/CNS integrated navigation system.