7Li and 71Ga NMR measurements have been performed to study the Li+ ionic motion and vacancy ordering in the lithium semimetal beta-LiGa. The temperature dependence of the spin-lattice relaxation rate, T1(-1) of the 7Li nuclei in the 50 atom% Li sample shows an asymmetric broad peak around 175 K and is interpreted in terms of fast Li ionic diffusion. The activation energy of hopping is estimated as 0.11 eV using a non-Debye type relaxation model. In the temperature dependence of T1(-1) of the 7Li nuclei in 44 and 47 atom% Li samples, steep peaks are observed at 225 and 195 K, respectively. The origin of these anomalous peaks is attributed to the order-disorder transformation of Li+ vacancies. The temperature dependence of T1(-1) of the 71Ga nuclei measured above 200 K is interpreted in terms of the relaxation originating from the fluctuation of the electric field gradient at the 71Ga nuclei due to mobile Li+ ions. The activation energy for the Li+ ionic diffusion estimated from T1(-1) of the 71Ga nuclei is comparable with that obtained from T1(-1) of the 7Li nuclei.