The microwave spectrum of the NBr radical in the X (3)Sigma(-) ground electronic state has been observed by a source modulated spectrometer. The NBr radical was generated in a free space cell by a de glow discharge in a mixture of N-2, Br-2, and He. The spectrum with three spin components of both two isotopomers, (NBr)-Br-79 and (NBr)-Br-81, was observed. The spectrum showed complicated splitting by the hyperfine interactions due to both bromine and nitrogen nuclei. The molecular constants including the magnetic hyperfine and nuclear quadrupolar hyperfine interaction constants were determined by analyzing the observed spectrum. The spin density of the unpaired electrons was estimated from the observed hyperfine coupling constants to be 73.4% and 22.4% on the nitrogen and the bromine atoms, respectively.