Multifractal characteristics of 16-channel human electroencephalogram (EEG) signals under eye-closed rest are analyzed for the first time. The result shows that the EEGs from the different sites on the scalp have different multifractal characteristics and the multifractal strength value Δα exhibits a kind of interleaving and left-right opposite distribution on scalp. This distribution rule is consistent with the localization of function and the lateralization theory in physiology. SoΔα can become an effective parameter to describe the brain potential character. And such a Δα stable distribution rule on sites of the scalp means a classic cerebral cortex active state.