The fluorescence (FL) system of the Tb^(3+)-sodium dodecylbenzene sulfonate (SDBS)- norepinephrine (NorEPN) was investigated. It was observed that the FL intensity of the Tb3+-SDBS was greatly enhanced by the NorEPN in presence of buffer. Based on this phenomenon, a simple and sensitive fluorimetric method for the quantitative determination of NorEPN was established. The FL intensity was measured with the excitation and emission wavelength of 290 nm and 545 nm respectively. Under optimum conditions, the enhanced FL intensity of the system was linear with the concentration of NorEPN in the range of 2.8×10^(-10) to 2.6×10^(-8) mol/L with a limit of detection (3σ) of 2.6×10^(-10) mol/L. The relative standard deviation (RSD) was 1.35% (n=9).