This paper discusses the accuracy analysis of the Monte Carlo (MC) method and its application in the arithmetic average Asian option pricing. First of all, we analyze the accuracy of the MC method and discuss two kinds of convergence in distribution to the standard normal distribution (namely standardizing the sample mean with the standard deviation and the standard error). Furthermore, we discuss the accuracy and the standard deviation (error) of the three kinds of MC methods (namely Crude MC, Antithetic MC, and Control MC). Then, we introduce the application of the MC method in the calculation of Asian option price. Finally, the numerical simulations of the arithmetic average Asian call option price show the following results: the two simulated success frequencies are both close to the theoretical probabilities; when the sample mean is standardized to be the standard normal distribution, the standard deviation is better than the standard error.