In this paper, we consider a discrete time stochastic Stackelberg game where there is a defender (also called leader) who has to defend a target and an attacker (also called follower). The attacker has a private type that evolves as a controlled Markov process. The objective is to compute Stochastic Stackelberg equilibrium of the game where defender commits to a strategy. The attacker's strategy is the best response to defender strategy and defender's strategy is optimum given attacker plays best response. In general computing such equilibrium involves solving a fixed-point equation for the whole game. In this paper, we present an algorithm that computes such strategies by solving smaller fixed-point equations for each time t. This reduces the computational complexity of the problem from double exponential in time to linear in time. Based on this algorithm, we compute Stackelberg equilibrium of a security example.