The pricing of moving window Asian option with an early exercise feature is considered a challenging problem in option pricing. The computational challenge lies in the unknown optimal exercise strategy and in the high dimensionality required for approximating the early exercise boundary. We use sparse grid basis functions in the Least Squares Monte Carlo approach to solve this “curse of dimensionality” problem. The resulting algorithm provides a general and convergent method for pricing moving window Asian options. The sparse grid technique presented in this paper can be generalized to pricing other high-dimensional, early-exercisable derivatives.