A tripodal quinone-cyanine dye having one donor and three acceptors, that is, one quinone and three N-methylbenzothiazolium moieties, QCy(MeBT)3, was synthesized by simple Knoevenagel condensation between 2-hydroxybenzene-1,3,5-tricarbaldehyde and N-methyl-2-methylbenzothiazolium iodide. The 700 nm (λex, 570 nm) and 600 nm (λex, 470 nm) fluorescence emission of QCy(MeBT)3 was significantly and individually enhanced with the addition of G-quadruplex (G4) DNA and double-stranded DNA (dsDNA), respectively. The results of docking simulations and the response against the viscosity change revealed that the dual-fluorescence response was caused by the difference in the binding mode of QCy(MeBT)3 depending on the DNA structure. The results of fluorescence microscopy imaging experiments using QCy(MeBT)3 suggested that G4 DNAs and dsDNAs in the cell nucleus can be imaged with near-infrared (NIR, 700 nm) and red (600 nm) fluorescence emissions. Furthermore, pyridostatin-induced G4 formation in the living cells can be imaged with NIR fluorescence. The results indicated that QCy(MeBT)3 has huge potential to be a NIR-fluorescent molecular probe for analyzing the structural dynamics of nucleic acids in living cells with a normal fluorescence microscope.