The lithium ion diffusion coefficient of a 93% Li β-alumina single crystal was measured for the first time using pulsed field gradient (PFG) NMR spectroscopy with two different crystal orientations. The diffusion coefficient was found to be 1.2 × 10-11 m2/s in the direction perpendicular to the c axis at room temperature. The Li ion diffusion coefficient along the c axis direction was found to be very small (6.4 × 10-13 m2/s at 333 K), which suggests that the macroscopic diffusion of the Li ion in the β-alumina crystal is mainly two-dimensional. The diffusion coefficient for the same sample was also estimated using NMR line narrowing data and impedance measurements. The impedance data show reasonable agreement with PFG-NMR data, while the line narrowing measurements provided a lower value for the diffusion coefficient. Line narrowing measurements also provided a relatively low value for the activation energy and pre-exponential factor. The temperature dependent diffusion coefficient was obtained in the temperature range 297-333 K by PFG-NMR, from which the activation energy for diffusion of the Li ion was estimated. The activation energy obtained by PFG-NMR was smaller than that obtained by impedance measurements, which suggests that thermally activated defect formation energy exists for 93% Li β-alumina single crystals. The diffusion time dependence of the diffusion coefficient was observed for the Li ion in the 93% Li β-alumina single crystal by means of PFG-NMR experiments. Motion of Li ion in fractal dimension might be a possible explanation for the observed diffusion time dependence of the diffusion coefficient in the 93% Li β-alumina system.