The diffusion coefficient of Li⁺ ions (D_Li) in the battery material Li_xCoO₂ has been investigated by means of muon-spin relaxation (μ⁺SR), because D_Li for positive electrode materials has not been determined correctly so far. Based on performing the experiments in zero-field and weak longitudinal-fields at temperatures up to 400 K, we determined the fluctuation rate (v) of the fields on the muons due to their interaction with the nuclear moments. Combined with susceptibility data and electrostatic potential calculations, clear Li⁺ ion diffusion was detected above ~ 150 K. The D_Li estimated from v was in very good agreement with predictions from first-principles calculations, and we present the μ⁺SR technique as a novel and optimal probe to detect D_Li of unique usefulness for materials containing magnetic ions.