A transition-density-fragment interaction (TDFI) combined with a transfer integral (TI) method is proposed. The TDFI method was previously developed for describing electronic Coulomb interaction, which was applied to excitation-energy transfer (EET) [K. J. Fujimoto and S. Hayashi, J. Am. Chem. Soc. 131, 14152 (2009)] and exciton-coupled circular dichroism spectra [K. J. Fujimoto, J. Chem. Phys. 133, 124101 (2010)]. In the present study, the TDFI method is extended to the exchange interaction, and hence it is combined with the TI method for applying to the EET via charge-transfer (CT) states. In this scheme, the overlap correction is also taken into account. To check the TDFI-TI accuracy, several test calculations are performed to an ethylene dimer. As a result, the TDFI-TI method gives a much improved description of the electronic coupling, compared with the previous TDFI method. Based on the successful description of the electronic coupling, the decomposition analysis is also performed with the TDFI-TI method. The present analysis clearly shows a large contribution from the Coulomb interaction in most of the cases, and a significant influence of the CT states at the small separation. In addition, the exchange interaction is found to be small in this system. The present approach is useful for analyzing and understanding the mechanism of EET.