Abstract: The enhanced Loran (eLoran) system is complementary to the Global Navigation Satellite System (GNSS), making it the best backup system. The receiver performs timing and positioning by measuring time of arrival (TOA). Noise is an important factor affecting the TOA accuracy of eLoran signal, and white Gaussian noise (WGN) is ubiquitous in noise. This paper based on the maximum likelihood estimation method was deduced under WGN of TOA error model, then using the method of linear congruence and Box - Muller transform method to generate WGN, the simulation analysis of the time and frequency domain properties of a gaussian white noise, the use of noise simulating TOA measurement error, and comparing with theoretical TOA model, The results show that the theoretical error model is consistent with the simulation TOA value error, which verifies the correctness of the TOA measurement error model and noise generation studied in this paper. The research results of this paper can provide reference for the TOA error model of eLoran signal and noise generation in the simulator, and promote the application development of eLoran system.