In this study, we build a Markov chain model for the earthquakes in Southwestern China by following the maximum entropy principle while the states of Markov chain are the co-occurrence of earthquakes with different magnitudes. In this case, an approximation is to focus on just the occurrences of the most serious magnitude earthquakes and neglect the others. Our approximation to this situation is to take all magnitude earthquakes into account if they occur at least once in any given period. In order to reveal the feature of this Markov chain in respect of the first passage time distributions, we run a long-term simulation with the occurrences of all the 3 categories of earthquakes. Finally, we give both the fitted distributions and multinomial approximations for the distribution of the first passage time for some states.