A parallel program can yield nondeterministic execution, which increases the complexity and the difficulty in program testing. The mutation testing of a message passing parallel program is investigated, and an approach to transforming the weak mutation testing for the program is presented in this study with the purpose of improving the efficiency of the mutation testing. First, the mutation condition statements are built based on the type of statements and the changes resulted from mutating these statements. Then, a new program is formed by inserting all these mutation condition statements into the original program. As a result, the problem of the weak mutation testing of the original program can be transformed into that of covering the branches of the new program, therefore providing advantages of solving the problem of mutation testing by using previous methods of branch coverage. The proposed approach is applied to test eight benchmark message passing parallel programs, and the empirical results demonstrate that this new approach is not only feasible but also necessary.