We develop a quasi‐analytical pricing method for discretely sampled arithmetic Asian options. We derive an asymptotic approximation of the arithmetic average with the geometric average of lognormal variables. Numerical experiments show that the asymptotic approximation is accurate and the absolute error converges very quickly as the number of observations increases. The absolute error is of the order of 10−5 to 10−6 for daily average. We then derive quasi‐analytical formulas for arithmetic Asian options under the Black–Scholes framework, in which the probability density of the geometric average is used. Extensive experiments are conducted to compare the proposed method with the various existing semianalytical methods. The overall accuracy of the proposed method is better than any other methods tested. The proposed method performs much better than the second best one for at‐the‐money Asian options under high volatility. The mean pricing error of the proposed method for a daily average Asian option is 37.5% less than the second best one.