A method of reconstructing perceived or imagined music by analyzing brain activity has not yet been established. As a first step toward developing such a method, we aimed to reconstruct the imagery of rhythm, which is one element of music. It has been reported that a periodic electroencephalogram (EEG) response is elicited while a human imagines a binary or ternary meter on a musical beat. However, it is not clear whether or not brain activity synchronizes with fully imagined beat and meter without auditory stimuli. To investigate neural entrainment to imagined rhythm during auditory imagery of beat and meter, we recorded EEG while nine participants (eight males and one female) imagined three types of rhythm without auditory stimuli but with visual timing, and then we analyzed the amplitude spectra of the EEG. We also recorded EEG while the participants only gazed at the visual timing as a control condition to confirm the visual effect. Furthermore, we derived features of the EEG using canonical correlation analysis (CCA) and conducted an experiment to individually classify the three types of imagined rhythm from the EEG. The results showed that classification accuracies exceeded the chance level in all participants. These results suggest that auditory imagery of meter elicits a periodic EEG response that changes at the imagined beat and meter frequency even in the fully imagined conditions. This study represents the first step toward the realization of a method for reconstructing the imagined music from brain activity.