Fluorescent DNA-binding dyes are extensively employed as probe and biosensing in biological detection and imaging. Experiments and theoretical calculations of thiazole orange homodimeric (TOTO) dye binding to a single-strand DNA (ssDNA), poly(dG)(n) (n = 2, 4, 6, 8), reveal that the n = 6 complex shows about 300-fold stronger fluorescence than n = 2, 4 and a slightly stronger one than n = 8 complexes, which is benefited from the length match between TOTO and poly(dG)(6). The machine learning, based on molecular dynamics trajectories, indicates that TOTO is featured by the dihedral angle along its backbone and its end-to-end distance, in which the latter one defines the stretch and hairpin structures of TOTO, respectively. The time-dependent density functional theory calculations on the low-lying excited states show that the stretched TOTO with pi-pi end-stacking binding mode can bring about strong fluorescence with localized pi-pi* transitions. For the n = 2, 4, and 8 complexes, the linear scaling quantum mechanics calculations indicate that the dominant hairpin TOTO with intercalative binding modes have relatively larger binding energies, leading to fluorescence quenching by intramolecular charge transfer. Our results may provide an insight for modulating the DNA-dye binding modes to tune the degree of charge transfer and designing fluorescent probes for the recognition of specific DNA sequences.