In this research, we consider the pricing of American options when the price dynamics of the underlying risky assets is governed by Markovian regime switching process. We assume that the price dynamics depends on the economy, the state of which transits based on a discrete-time Markov chain. The underlying economy cannot be known directly but can be partially observed by receiving a signal stochastically related to the real state of economy. The pricing procedure and optimal stopping problem are formulated using partially observable Markov decision process, and some structural properties of the resulting optimal expected payoff functions are derived under certain assumptions. These properties establish the existence of a monotonic policy with respect to the holding time, asset price, and economic conditions.