The H-NMR 1 -NMR measurements were carried out on the organic conductor, (BEDT-TTF) 3 CuBr 4 , where strong coupling between π and 3d electrons are expected. The H 1 spin-lattice relaxation rate, T 1 - 1 , was large about 20 sec - 1 and almost temperature independent above 60 K indicating the effect of localized magnetic moments. Anomalies at the structural transition (60 K) was small. An antiferromagnetic transition was confirmed: The magnitude of the moment at Cu site was estimated as 0.6-0.7 μ B . The moment at the Cu site was found to survive in the metallic state under pressure.