Due to the potential application of DNA for biophysics and optoelectronics, the electronic energy states and transitions of this genetic material have attracted a great deal of attention recently. However, the fluorescence and corresponding physical process of DNA under optical excitation with photon energies below ultraviolet are still not fully clear. In this work, we experimentally investigate the photoluminescence (PL) properties of single-stranded DNA (ssDNA) samples under near-ultraviolet (NUV) and visible excitations (270∼440 nm). Based on the dependence of the PL peak wavelength (λ_{em}) upon the excitation wavelength (λ_{ex}), the PL behaviors of ssDNA can be approximately classified into two categories. In the relatively short excitation wavelength regime, λ_{em} is nearly constant due to exciton-like transitions associated with delocalized excitonic states and excimer states. In the relatively long excitation wavelength range, a linear relation of λ_{em}=Aλ_{ex}+B with A>0 or A<0 can be observed, which comes from electronic transitions related to coupled vibrational-electronic levels. Moreover, the transition channels in different excitation wavelength regimes and the effects of strand length and base type can be analyzed on the basis of these results. These important findings not only can give a general description of the electronic energy states and transitional behaviors of ssDNA samples under NUV and visible excitations, but also can be the basis for the application of DNA in nanoelectronics and optoelectronics.