The precision of the strapdown inertial navigation system (SINS) depended on the work precision of the gyroscope. However, many errors affect the precision of SINS even if the gyroscopes have perfect principles and structures. Before the application of the inertial navigation system (INS), the inertial components must be calibrated to ensure the performance of components, detect whether the precision of the inertial component satisfied the system, and compensate for the error of INS. According to the mathematical model of fiber optic gyroscope (FOG), we propose a multi-position iterative recursive calibration algorithm to compensate for the error of scale factor and installation of FOG. To guarantee the accuracy of the SINS, the error mathematical model of the FOG is established and compensated in the system. Finally, the calibration parameters of FOG are calibrated by the multi-position iterative recursive calibration (MPIRC) and the six-position method. The calibration results show that the accuracy of components calibration parameters of the MPIRC and the six-position is similar, but the accuracy of SINS using MPIRC is higher than that using six-position.