Asymmetric cyanine fluorescent dyes are represented by general formula I. These kinds of dyes may be used as a staining agent for nucleic acids, with the spectra at 600-900 nm in the near-infrared region and without interference from background fluorescence. These kinds of dyes may be useful with small-type red semiconductor lasers as the light source (such as 633 nm). Compositions comprising these dyes and methods for staining biological samples using these dyes or compositions are also provided.