Abstract: Current ratio error and phase error, which are impacted by noise, are fundamental index of current sensor. Compared with conventional current sensor, optical fiber current sensor contains much more noise, thus has lower measurement accuracy for small signal. This has restricting practical use for optical fiber current sensor. Statistical characteristic of current ratio error and phase error under white Gaussian noise was analyzed, so was the standard of signal to noise ratio(SNR) when it can meet 0.2 accuracy class. Furthermore, formula of SNR was deduced and influencing factors of SNR was discussed. Theoretical analysis and experiments indicate that the SNR of optical fiber needs to be 29 dB to meet the demand of 0.2 accuracy class. When the rated current and update rate are confirmed, only reducing noise and increasing the number of loops of optical fiber current sensor can improve SNR.