Brain-computer interface (BCI) studies based on electroencephalography (EEG) measured around the ears (ear-EEGs) have mostly used exogenous paradigms involving brain activity evoked by external stimuli. The objective of this study is to investigate the feasibility of ear-EEGs for development of an endogenous BCI system that uses self-modulated brain activity. We performed preliminary and main experiments where EEGs were measured on the scalp and behind the ears to check the reliability of ear-EEGs as compared to scalp-EEGs. In the preliminary and main experiments, subjects performed eyes-open and eyes-closed tasks, and they performed mental arithmetic (MA) and light cognitive (LC) tasks, respectively. For data analysis, the brain area was divided into four regions of interest (ROIs) (i.e., frontal, central, occipital, and ear area). The preliminary experiment showed that the degree of alpha activity increase of the ear area with eyes closed is comparable to those of other ROIs (occipital > ear > central > frontal). In the main experiment, similar event-related (de)synchronization (ERD/ERS) patterns were observed between the four ROIs during MA and LC, and all ROIs showed the mean classification accuracies above 70% required for effective binary communication (MA vs. LC) (occipital = ear = central = frontal). From the results, we demonstrated that ear-EEG can be used to develop an endogenous BCI system based on cognitive tasks without external stimuli, which allows the usability of ear-EEGs to be extended.