A novel fluorimetric method was developed for the rapid determination of DNA and RNA based on their quenching effect on the cationic red-region fluorescent dye Nile Blue (NB). In the investigation of the interaction of NB with DNA by steady-state polarization measurements, thermal denaturing study, determination of absorption and fluorescence characteristics, salt effect study and electrophoresis experiments, the results supported the suggestion that NB served as an intercalator to the stack base pairs of nucleic acids. Further evidence showed that the quenching could be ascribed to the static quenching mode. A binding constant of about 10⁶ M^–1 and a binding site size of about three base pairs were obtained by spectral methods. Under optimum conditions, the calibration curves for the determination of calf thymus DNA (CT DNA) and yeast RNA were linear over the ranges 3.0 ng mL^–1–2.0 µg mL^–1 and 27 ng mL^–1–10 µg mL^–1, respectively. The detection limits were 3.0 ng mL^–1 for CT DNA and 27 ng mL^–1 for RNA. The relative standard deviation (n = 6) was within 2.1% in the middle of the linear range. Interferences from some interesting co-existing substances in the determination of DNA were also examined.