The early Parkinson's disease (PD) with mild cognitive impairment (ePD-MCI) is a typical non-motor symptom reflected by the brain dysfunction of PD, which can be well depicted by the dynamic characteristics of brain functional connectivity networks. The aim of this study is to determine the unclear dynamic changes in functional connectivity networks induced by MCI in early PD patients. In this paper, the electroencephalogram (EEG) of each subject was reconstructed into the dynamic functional connectivity networks with five frequency bands based on adaptive sliding window method. By evaluating the fluctuations of dynamic functional connectivity and the transition stability of functional network state in ePD-MCI patients compared with early PD without mild cognitive impairment patients, it was found that in the alpha band, the functional network stability of central region, right frontal, parietal, occipital, and left temporal lobes was abnormally increased, and the dynamic connectivity fluctuations in these regions were significantly decreased in ePD-MCI group. In the gamma band, ePD-MCI patients showed decreased functional network stability in the central, left frontal, and right temporal lobes, and active dynamic connectivity fluctuations in the left frontal, temporal, and parietal lobes. The aberrant duration of network state in ePD-MCI patients was significantly negatively correlated with cognitive function in the alpha band, which might pave the way to identify and predict cognitive impairment in early PD patients.