In a paramagnetic state of Li2MnO3, i.e. at temperatures above T-N = 35 K, muon-spin relaxation (mu+SR) measurements with zero applied magnetic field (ZF) and longitudinal-field (LF) revealed the presence of a dynamic fluctuation of a nuclear magnetic field due to Li+-diffusion. From the motional narrowing behavior of the field distribution width, the Li+ ions were found to diffuse mainly along the c-axis through the Li+ ion in the [Li1/3Mn2/3]O-2 layer. Also, based on the field fluctuation rate, a self-diffusion coefficient of Li+ ions (D-Li) at 300 K was estimated as 4.7(4) x 10(-11) cm(2)/s with the thermal activation energy E-alpha = 0.156(3)eV. (C) 2013 Elsevier B.V. All rights reserved.