Electroencephalogram (EEG), the measures and records of the electrical activity of the brain, exhibits evidently nonlinear, non-stationary, chaotic and complex dynamic properties. Based on these properties, many nonlinear dynamical analysis techniques have emerged, and much valuable information has been extracted from complex EEG signals using these nonlinear analysis techniques. Among these techniques, the Hurst exponent estimation was widely used to characterize the fractional or scaling property of the EEG signals. However, the constant Hurst exponent H cannot capture the the detailed information of dynamic EEG signals. In this research, the multifractional property of the normal human sleep EEG signals is investigated and characterized using local Hölder exponent H(t). The comparison of the analysis results for human sleep EEG signals in different stages using constant Hurst exponent H and the local Hölder exponent H(t) are summarized with tables and figures in the paper. The analysis results show that local Hölder exponent provides a novel and valid tool for dynamic assessment of brain activities in different sleep stages.