Ion-conducting garnets are important candidates for use in all-solid Li batteries and numerous materials have been synthesized with high ionic conductivities. For understanding ion conduction mechanisms, knowledge on Li+ diffusion behaviour is essential. The proposed nano-scale lithium pathways are composed of tortuous and narrow Li+ channels. The pulsed gradient spin-echo (PGSE) NMR method provides time-dependent 7Li diffusion on the micrometre space. For powder samples, collision-diffraction echo-attenuation plots were observed in a short observation time, which had not been fully explained. The diffraction patterns were reduced or disappeared for single-crystal garnet samples of Li6.5La3Zr1.5Ta0.5O12 (LLZO-Ta) and Li6.5La3Zr1.5Nb0.5O12 (LLZO-Nb). The inner morphology and grain boundaries affect importantly the collision-diffraction behaviours which is inherent to powder samples. The 7Li diffusion observed by PGSE-NMR depends on the observation time (Δ) and the pulsed field gradient (PFG) strength (g) in both powder and single-crystal samples, and the anomalous effects were reduced in the single-crystal samples. The scattered Li diffusion constants converged to a unique value (DLi) with a long Δ and a large g, which is eventually the smallest value. The DLi activation energy was close to that of the ionic conductivity (σ). The DLi values are plotted versus the σ values measured for four powder and two single-crystal garnet samples. Assuming the Nernst-Einstein (NE) relation which was derived for isolated ions in solution, the carrier numbers (NNE) were estimated from the experimental values of DLi and σ. The NNE values of metal-containing garnets were large (<1023 cm-3) and insensitive to temperature. They were larger than Li atomic numbers in cm3 calculated from the density, molecular formula and Avogadro number for LLZOs except for cubic LLZO (Li7La3Zr2O12, NNE∼ 1020 cm-3).