One of the resting state networks is the default mode network (DMN); the DMN is primarily concerned with self-perception, orientation, and memory. Although EEG-DMN has been suggested to be active in the ultra-low frequency band below 1 Hz based on fMRI studies, the characteristics of the network have not yet been elucidated. In this study, we measured EEG-DMN during the eye-closed resting state(EC), eye-open resting state(EO), and mental arithmetic with eye-close(CA), and analyzed network activity using phase locking value(PLV), an index of phase-locking, which is one of the functional connectivity. The results showed that functional connectivity between regions (frontal, central, posterior, occipital) including DMN-related regions in SubDelta (0.01-0.1Hz) was significantly higher during eye-closed resting state than during mental arithmetic with eye-close (EC PLV - CA PLV in Frontal-Posterior = 0.062). In contrast, in the high frequency band(Theta), PLV during mental arithmetic with eye-close was significantly higher than during eye-closed resting between Occipital-Right temporal (EC PLV – CA PLV in Posterior-Right temporal = -0.051). This finding is similar to previous studies and suggests that the analysis of functional connectivity in the very low-frequency band below 0.1 Hz can reveal EEG-DMN activity. This result indicates that DMN activity can be captured not only by fMRI and intracranial EEG (iEEG) but also by cortical EEG. This will contribute to the elucidation of the pathology of diseases with reported abnormal DMN activity, such as depression and dementia, as well as to the further elucidation of DMN function.