If you mean that he sings just using his voice, without any musical accompaniment, then "a capella".
If you mean that he sings without using the sheet music (words and notes on a piece of paper), then "from memory" or "by heart".
Really? OK, perhaps it's because I have a musical background (I was in an a capella singing group, and one of my relatives dated a member of The Flying Pickets, an a capella band who had a number one hit!)