Sound localization in the front-back dimension is reported to be challenging, with individual differences. We investigated whether auditory discrimination processing in the brain differs based on front-back sound localization ability. This study conducted an auditory oddball task using speakers in front of and behind the participants. We used event-related brain potentials to examine the deviance detection process between groups that could and could not discriminate front-back sound localization. The results indicated that mismatch negativity (MMN) occurred during the deviance detection process, and P2 amplitude differed between standard and deviant locations in both groups. However, the latency of MMN was shorter in the group that could discriminate front-back sounds than in the group that could not. Additionally, N1 amplitude increased for deviant locations compared to standard ones only in the discriminating group. In conclusion, the sensory memories matching process based on traces of previously presented stimuli (MMN, P2) occurred regardless of discrimination ability. However, the response to changes in the physical properties of sounds (MMN latency, N1 amplitude) differed depending on the ability to discriminate front-back sounds. Our findings suggest that the brain may have different processing strategies for the two directions even without subjective recognition of the front-back direction of incoming sounds.