Right-ear advantage refers to the observation that when two different speech stimuli are simultaneously presented to both ears, listeners report stimuli more correctly from the right ear than the left. It is assumed to result from prominent projection along the auditory pathways to the contralateral hemisphere and the dominance of the left auditory cortex for the perception of speech elements. Our study aimed to investigate the role of attention in the right-ear advantage. We recorded magnetoencephalography data while participants listened to pairs of Japanese two-syllable words (namely, "/ta/ /ko/" or "/i/ /ka/"). The amplitudes of the stimuli were modulated at 35 Hz in one ear and 45 Hz in the other. Such frequency-tagging allowed the selective quantification of left and right auditory cortex responses to left and right ear stimuli. Behavioral tests confirmed the right-ear advantage, with higher accuracy for stimuli presented to the right ear than to the left. The amplitude of the auditory steady-state response was larger when attending to the stimuli compared to passive listening. We detected a correlation between the attention-related increase in the amplitude of the auditory steady-state response and the laterality index of behavioral accuracy. The right-ear advantage in the free-response dichotic listening was also found in neural activities in the left auditory cortex, suggesting that it was related to the allocation of attention to both ears.