This paper employs a stochastic endogenous growth model with productive govment expenditure in a small open economy to analyze the optimal fiscal policy.First,a stochastic model of a small open economy is constructed.Second.the equilibrium solutions of the representative agent’s stochastic optimization problem are derived.Third,we obtain the equilibrium solutions of the central planner’s stochastic optimization problem and the optimal govment expenditure policy.Finally,the optimal tax policy is characterized.