On the basis of the reliable B3LYP/6-311+G* method, four kinds of coupling modes for the complexes of imidazole and imidazole cation are found through the geometry optimizations. In total, 19 stable complexes are found on the global potential energy surfaces, and they may be classified as: (CN)-N-... mode, (NN)-N-... mode, single H-bond mode, and double H-bond mode. The harmonic vibrational frequency, charge population, and spin density analyses are carried out, and the coupling character of each complex is analyzed. Optimizations have indicated the spontaneous proton transfers between two moieties of each complex that includes the N-(HN)-N-... type H-bond. The relative stability after the BSSE and ZPE corrections is compared, and the most stable complexes are those with N-(HN)-N-... type H-bonds. The calculated adiabatic electron affinities, E-A, of these complexes are near 180.0 kcal/mol, and the EA of the complex with the linear C-(HN)-N-... type H-bond is the biggest while that with proton transfer is the smallest. The difference of the E(A)s and vertical E(A)s (VEAS) and their origins are compared. The deformation energies of the (CN)-N-... covalent mode complexes are larger while those of the double H-bond mode complexes are smaller. Preliminary analyses indicate that there are many possible interaction modes among different biological fragments and the different coupling modes may yield different effect on the biomolecule structures and further regulate their functionality and reactivity mechanism.