Multi-oscillator ring laser gyro has no moving part in comparing with dither biased ring laser gyro, thus it is very suitable for wide band vibration measurement. Random noise in the output of ring laser gyro will constrain its performance dramatically. The random noise can be typically divided into quantization noise, white rate noise, bias instability (1/f or flicker rate), rate random walk and flicker rate ramp etc.. Allan variance method is a powerful tool in the time domain for the analysis of random noise, but because different noise has different correlation time, the Allan Variance need long test time such as more than a few hours. A noise analysis method of multi-oscillator ring laser gyro based on power spectral density (PSD) is put forward which need very short test time than Allan Variance method. the analyze is carried out in frequency domain other than time domain, curve fitting method is then used to get noise coefficients. Contrast experiments with the Allan variance analysis method are carried out. The results show that the noise coefficients calculated by the PSD method in which the test time is a few seconds are in good agreement with the coefficients calculated by Allan variance method in which the test time is 16384 seconds. Thus, it is feasible to calculated angle random walk coefficient by the PSD method. Moreover, due to less test time, the trend of the noise coefficients can also be observed by this new method.