Systematic measurements of H-NMR 1 -NMR relaxation rate, T 1 - 1 , in the organic conductor, (DMe-DCNQI-d 7 ) 2 Cu 1 - x Li x (x = 0.04, 0.5 ∼ 0.6, 1), have been carried out, to clarify the effect of Li doping on the electronic properties of pπ-band. Within the stable metallic region (up to about x = 0.5), T 1 - 1 exhibits a Korringa-like behavior, (T 1 T) - 1 = const. In a highly doped sample, a nonmetallic phase appears at low temperatures. The absolute value of T 1 - 1 in the metallic region increases remarkably with the Li concentration and becomes the largest in the pure Li-salt, (DMe-DCNQI-d 7 ) 2 Li. This behavior is analyzed as a low-dimensional spin-diffusion effect.