The excitation energy transfer from meso-tetrakis(N-methylpyridinium-4-yl)porphyrin (TMPyP) to 3,3'-diethyl-2,2'-thiatricarbocyanine iodide (DTTCI) along the deoxyribonucleic acid (DNA) double strand was investigated by the steady-state absorption and fluorescence measurements and time-resolved fluorescence measurements. The steady-state fluorescence spectra showed that the near-infrared fluorescence of DTTCI was strongly enhanced up to 86 times due to the energy transfer from the excited TMPyP molecule in DNA buffer solution. Furthermore, we elucidated the mechanism of fluorescence quenching and enhancement by the direct observation of energy transfer using the time-resolved measurements. The fluorescence quenching of TMPyP chiefly consists of a static component due to the formation of complex and dynamic components due to the excitation energy transfer. In a heterogeneous one-dimensional system such as a DNA chain, it was proved that the energy transfer process only carries out within the critical distance based on the Forster theory and within a threshold value estimated from the modified Stern-Volmer equation. The present results showed that DNA chain is one of the most powerful tools for nanoassemblies and will give a novel concepts of material design.