A new method producing Gaussian white noise is presented based on the summation law of central limit theorem. The characteristics of Gaussian white noise are analyzed. The Gaussian random sequence generated by the uniformly distributed random sequence summation is analyzed to extract its time domain and frequency domain features, and then compared with the random sequence generated by randn function of Matlab. Gaussian random sequence generated by summation law is tested by testing. Experiment results show that the random number generated by summation law is very similar to Gaussian distribution white noise.