Microscopic magnetism of the electrochemically Li-deintercaleted Li x CoO2 powders has been investigated by muon-spin rotation and relaxation (μ+SR) spectroscopy in the temperature (T) range between 10 and 300K. Weak transverse-field μ+SR measurements indicate that localized moments appear in LiCoO2 below 60K, while both Li0.53CoO2 and Li0.04CoO2 are paramagnetic even at 10K. Zero-field μ+SR measurements for the samples with x =0.53 and 0.04 show that the field distribution width (Δ) due to randomly oriented nuclear magnetic moments of 7Li and 59Co decreases monotonically with increasing T up to 250K, and then it decreases steeper (increasing slope (dΔ/dT)) above 250K. Because the muon hopping rate (ν) is almost T independent for Li0.53CoO2 below 300K, the decrease in Δ suggests that the time scale of Li+ diffusion in Li x CoO2 is within a microsecond scale.