Abstract: The kernel of option theory is the option pricing problem. To price the continuously sampled arithmetic average Asian option, an implicit upwind difference scheme is constructed based on the final boundary value problem of partial differential equation, which is satisfiable to the option pricing problem. Then the unique existence and unconditional stability of the difference solution are demonstrated and the error estimate is given under the discrete L2 norm. Some numerical examples are given to show that the numerical method presented is an approximation method with high efficiency and convergence.