By using the imaginary-time propagation method, we study the ground state structure of a two-component dipolar Bose-Einstein condensate confined in a coupled annular potential. The effects of contact and dipole-dipole interaction on the ground state density distribution of such a system are investigated in detail. The results show that the dipole-dipole interaction, acting as a new degree of freedom, can be used to obtain the desired ground state phases, and to control the phase transition between different ground states.