Numerous investigations have evidenced that human brain network may be operated in a critical state. Here we investigated whether the resting brain with eyes-close state was more likely a critical state than eyes-open state by using EEG recording technique and subsequent frequency domain analysis. EEGs of 26 healthy subjects (mean age ± SD 21.54 ± 3.70) during eyes-close and eyes-open state were collected. Then we analyzed the power law distribution of cascades size and duration and calculated the branch parameter of the EEG data in frequency domain. We found the critical exponent of cascade size and cascade duration of eyes-close state were consistently lower than that in the eyes-open state for different time-windows, and the branch parameter showed consistent results. The critical exponents of the distributed avalanche sizes and durations during eyes-close state were observed around -1.5 and -2 respectively for a certain time window, correspondingly, the branch parameter was approached 1. This indicated that the brain activity dynamic of eyes-close state was more likely around criticality, while eyes-open brain dynamics was inclined to a supercritical state.