High-resolution fluorescence imaging of lambda-phage DNA molecules, intercalated with the dye YOYO-1, has been performed by a SNOM/AFM based on a bent-type optical fiber probe. A modified design of the optical probe has been made, and successful near-field optical resolution has been obtained for the strongly stretched lambda-phage DNA molecules. The best optical resolution was estimated at 45 nm for the dye-intercalated single lambda-DNA molecules by a mean width evaluation. In our comparison between the far-field fluorescence and high-resolution near-field fluorescence images for the DNA, it has been found that the near-field images much better defined the intercalation state of the dye. Finally, the relation between the DNA shapes and the dye distribution states, and the discrimination between the double-stranded and single-stranded DNA molecules, are discussed by comparing the topography and fluorescence images of the SNOM/AFM.