Modified Cox-Ingersoll-Ross model is employed, combining with Hamilton (1989) type Markov regime switching framework, to study foreign exchange rates, where all parameter values depend on the value of a continuous time Markov chain. Basing on real data of some foreign exchange rates, the Expectation-Maximization algorithm is extended to this more general model and it is applied to calibrate all parameters. We compare the obtained results regarding to results obtained with non regime switching models and notice that our results match much better the reality than the others without Markov switching. Furthermore, we illustrate our model on various foreign exchange rate data and clarify some significant eco- nomic time periods in which financial or economic crisis appeared, thus, regime switching obtained.