In this chapter, we consider the problem of American option pricing when the asset price dynamics follow a binomial model dominated by a varying economic situation. We assume that the economic situation transits based on a semi-Markov chain. The pricing procedure is formulated using a semi-Markov decision process, as the decision-maker decides whether to exercise early or hold the option. Some properties of the optimal exercise regions and the monotonicity of option prices are discussed based on simulation results when each parameter is changed, and the optimal strategies are investigated.