Computation of approximation is a critical step for applying rough sets methodologies in knowledge discovery and data mining. As an extension of classic rough sets theory, Dominance-based Rough Sets Approach (DRSA) can process information with preference-ordered attribute domain and then can be applied in multi-criteria decision analysis and other related works. Efficiently computing approximations is helpful for reducing the time of making decisions based on DRSA. Parallel computing is an effective way to speed up the process of computation. In this paper, several strategies of decomposition and composition of granules in DRSA are proposed for computing approximations in parallel and the corresponding parallel algorithm is designed. A numerical example is employed to validate the feasibility of these strategies. The experimental evaluations on a multi-core environment showed that the parallel algorithm can obviously reduce the time of computing approximations in DRSA.