In this talk, an efficient and accurate numerical method is developed to compute ground states of a novel rotating BEC-impurity system. The key idea is twofold. First, since the impurities are localized in a small box potential, two grids are designed to compute the ground states of the model problem, i.e., a general grid for a suitable large domain to compute the wave function of BEC and an imbedded grid for a small domain determined by the size of a box potential to calculate the wave functions of impurities. Then, a preconditioned conjugate gradient (PCG) method is applied to solve the ground states of the rotating BEC-impurity system. Extensive numerical results of ground states for the BEC-impurity system are reported to show the efficiency of our method and demonstrate interesting physical phenomena.