A theoretical composite-molecule (CM) model is adopted for evaluating the electronic excited states and excitonic couplings of cofacial conjugated dimers where the contributions of charge-transfer (CT) exciton, unavailable by the commonly used supermolecular approach due to the inadequate basis set construction, can be unambiguously identified within this methodology. This method builds up with the basis set of individual molecules and then constructs combined electronic states for the dimer by considering intermolecular interactions including charge-transfer interactions. The dependences of the matrix elements on intermolecular distance and conjugation length are examined. At the short distance region between two of the polyene molecules in the dimer, the CT transitions are apparently mixing to both first and second excited states. Also, some of the matrix elements for the mixing of CT transitions with local transitions which related to the second excited state are found to be considerably larger than the exciton-type elements. An interesting finding is that with increasing the chain size the CT contribution to the second excited state reveals a minimum and indicates HOMO to LUMO charge transfer is not the major CT contribution to the second excited state in the face-to-face polyene dimer with larger chain size and interchain separation in the region of 3.6-4.0 A. A detail analysis reveals that HOMO-1 to LUMO and HOMO to LUMO+1 charge transfers are major CT contributions to the second excited state in the condition under study.