It is found that silver nanoparticles (AgNPs) can further enhance the fluorescence intensity of curcumin (CU) - cetyltrimethylammonium bromide (CTAB) – nucleic acids and improve its anti-photobleaching activity. Under optimum conditions, the enhanced fluorescence intensity is proportion to the concentration of nucleic acids in the range of 2.0 × 10⁻⁸–1.0 × 10⁻⁶ g mL⁻¹ for fish sperm DNA (fsDNA), 2.0 × 10⁻⁸–1.0 × 10⁻⁶ g mL⁻¹ for calf thymus DNA (ctDNA), 1.0 × 10⁻⁸–1.0 × 10⁻⁶ g mL⁻¹ for yeast RNA (yRNA), and their detection limits (S/N = 3) are 8.0 ng mL⁻¹, 10.5 ng mL⁻¹ and 5.8 ng mL⁻¹, respectively. This method is used for determining the concentration of DNA in actual sample with satisfactory results. The interaction mechanism is also studied.