A diffusive behavior of Li+ ion in a garnet-type oxide, Li(5 + x)La(3)Zr(x)Nb(2 - x)0(12) with x = 0-2, has been investigated by both a positive muon-spin relaxation (mu+SR) and quasi-elastic neutron scattering (QENS) technique using powder samples. The mu+SR results revealed that Li+ ions start to diffuse above similar to 150 K for the whole samples measured. The activation energy of Li diffusion (E-a) estimated from the mu+SR data was in good agreement with E-a obtained by the QENS measurements. However, both E(a)s were about a half of E-a of ionic conductivity of Li+ (sigma(Li)), which was evaluated by AC-impedance measurements on sintered pellets. This indicated the serious effect of grain boundary and/or surface on E-a. Furthermore, since the diffusion coefficient of Li+ estimated by mu+SR is roughly independent of x, the number of mobile Li+ in the garnet lattice was found to be the predominant parameter to determine sigma(Li). (C) 2013 Elsevier B.V. All rights reserved.