There is some background noise but it's not too bad. The recording is actually of a high quality and I like the accoustic guitar sound you've achieved. I'd recommend I little more compression on the vocals just to keep that slight jump in volume when you sing that very long note in check. You can't actually hear the background noise (and I emphasise background noise, I don't hear much miss but I'm listening to this at work on crappy headphones) when the singing starts. However, it's recorded room noise - I suspect you have a light or something near by that making a low noise which is hard for the human ear to pick up but which the mic is picking up. To be honest I doubt it's noticable enough to bother with re-recording the tracks. There is a ringing type noise which is evident after the final strum of the guitar. If the resonance of the playing is making a vase, glass or something else near by vibrate that could be the cause.
Nice work though - beautiful playing and singing.