This is (partly) what meditation is for; shutting off the voice in your head. During the initial attempts, this seems impossible. When you do finally make it happen, your inner voice will probably cheer, ironically ending the experience quickly.
However, that small bit of silence can be used as encouragement, knowing that the goal is reachable. Once you're able to do it a few more times, it gets easier and easier. Eventually, you can get your brain to go silent almost instantly when you have a moment of stillness. The "voice" learns that it's beneficial to shut up and listen.
