The exciton transfer in light-harvesting complex with the following electron-hole separation in the photosynthetic reaction center dimer is investigated theoretically. The asymmetry in the ring structure of the LH1 antenna complex is assumed. The impact of this asymmetry on the exciton transfer is studying. The quantum yields of the electron-hole separation and the exciton deactivation into the ground state have been computed. It was shown that the asymmetry does not affect these quantum yields if the coupling between antenna ring molecules is strong enough. Exciton kinetics are different when the asymmetry is present, but the electron-hole separation efficiency is similar to the symmetric case.It was also showing that the creation of the dimer in the reaction center is advantageous to the case of the monomeric reaction center.