This paper considers the problem of matching between laboratories and students when there are two types of students, such as domestic and overseas students. Each laboratory has minimum and maximum quotas for the number of overseas students and the total number of students. When there is only one type of student, a strategyproof matching algorithm was shown by Fragiadakis et.al. Their algorithm uses a precedence list (PL) to achieve fairness and nonwastefulness properties. This paper generalizes the algorithm for the cases when there are two types of students. Our algorithm achieves fairness based on the PL-list, nonwastefulness, and strategyproofness.