Understanding the neural mechanisms underlying speech production has a number of potential practical applications. Speech production involves multiple feedback loops. An audio-vocal monitoring system plays an important role in speech production, based on auditory feedback about the speaker's own voice. Here we investigated the mu-rhythm activity associated with speech production by examining event-related desynchronization and synchronization in conditions of delayed auditory feedback (DAF) and noise feedback (Lombard). In Experiment 1, we confirmed that the mu-rhythms were detectable for a conventional finger-tapping task, and vocalization. In Experiment 2, we examined the mu-rhythms for imagined speech production. We tested whether the same motor-related mu-rhythm activity was exhibited while participants listened to their own voice, and while reading. The mu-rhythms were observed for overt vocalization and covert reading, while listening to simulated auditory feedback of the participants' own voice reading text. In addition, we found that the mu-rhythm associated with listening was boosted and attenuated under the DAF and Lombard conditions, respectively. This is consistent with the notion that auditory feedback is important for the audio-vocal monitoring system in speech production. This paradigm may help clarify the way in which auditory feedback supports motor planning, as indexed by the motor-related mu-rhythm.