Summary: In this paper, a Monte Carlo algorithm for estimating the price of Asian option under the stochastic volatility model is given. First, the formulas of the underlying assets paths and stochastic volatility paths are derived. Then, in order to reduce the simulation variance, the antithetic variable technique Monte Carlo simulation method is used to calculate the numerical solution of Asian option prices. We compared the numerical results of Asian option under stochastic volatility model and B-S model. Finally, some numerical results of the fixed strike and the floating strike arithmetic Asian option under stochastic volatility are given.