Is the buzz less when you have your hands on the strings? If so you may have a ground issue. I had a ground wire that broke off the trem on one of my guitars and the buzzing was horrible.
Do you have any appliances that are on the same circuit? A refrigerator or anything that cycles and is on all the time can make a terrible racket through your amp.
Have you removed and reinserted the tubes? Sometimes a buzzing sound can be from dirty tube contacts. Make sure the amp is unplugged when you try this
Sometimes a bad tube can cause it. Try putting in a new 12AX7 in the preamp positions and see if that helps. Again, unplug first.
I have a tube amp that is over 40 years old and doesn't buzz. My other tube amps that were over 12 years old never buzzed either. Wayne is right, though, if it's older it might need a recap, especially if it hasn't been used in a while. But I guess I've been fortunate and never had to recap yet.
Another issue might be the input jack on the amp itself. Bad solder joints could cause it.
And the end-all-be-all...do you have a local tech to look at it? If none of the above work take it to someone you trust to give it a look over.