This paper presents a numerical algorithm to calculate the first and second moments of the first passage times between states on a certain subset, which concern with the key measures of interests of the Markov renewal process with finite states. Since recursive formulas are the important part of the algorithm, it is very well suited to the computation of the moments and is easily programmed. The algorithm makes it possible to compute the key measure of interests on microprocessor even when the model comprised a quite large number of states.