To investigate the abnormal brain activities in the early stage of Parkinson's disease (PD), the electroencephalogram (EEG) signals were recorded with 20 channels from non-dementia PD patients (18 patients, 8 females) and age matched healthy controls (18 subjects, 8 females) during the resting state. Two methods based on the ordinal patterns of the recorded series, i.e., permutation entropy (PE) and order index (OI), were introduced to characterize the complexity of the cortical activities for two groups. It was observed that the resting-state EEG of PD patients showed lower PE and higher OI than healthy controls, which indicated that the early-stage PD caused the reduced complexity of EEG. We further applied two methods to determine the complexity of EEG rhythms in five sub-bands. The results showed that the gamma, beta and alpha rhythms of PD patients were characterized by lower PE and higher OI, i.e., reduced complexity, than healthy subjects. No significant differences were observed in theta or delta rhythms between two groups. The findings suggested that PE and OI were promising methods to detect the abnormal changes in the dynamics of EEG signals associated with early-stage PD. Further, such changes in EEG complexity may be the early markers of the cortical or subcortical dysfunction caused by PD.