Asian options have payoffs that depend strongly on the historical information of the underlying asset price. Although approximated closed-form formulas are available with various assumptions, most of them do not guarantee convergence. Binomial tree and partial differential equation (PDE) methods are two popular numerical solutions for pricing. However, both methods have a complexity of at least O(N ²), where N is the number of time steps. We propose a convergent lattice method with a complexity of O (N1.5), based on Curran's willow tree method. We also analyze the corresponding convergence rate and error bounds and show that our proposed method can provide the same accuracy as the PDE and binomial tree methods but requires much less computational time. When a quick pricing is required, our method can give the price to within one US cent in less than half a second. We give numerical results to support our claims.