It looks to me like a Singer 15-89 or 90. Go to the Vintage machine shop here, or PM Billy (Lostn51) our resident expert.
I have a 15-91 which doesn't have a belt- it's gear driven. and I love it. There are tutorials on how to clean and repair these machines on the Vintage thread, and Billy can tell you where to find parts- they are readily available.
Good luck, she's a beauty!