Such banding is not uncommon, you have a a few choices on how to proceed.
Option 1: try and fix the root cause of the problem -- the scanner.
Odds are there is a (very small) bit of dust on the scan head, try opening up the scanner and using a rocket blower or similar along the scan sensor. Of course this involves opening the thing up and depending on you and your experience this may not be something you want to try.
Option 2: fix it in post
Scan a completely black sheet of paper (or better yet get a print of an image of the same size and finish as the photos you are scanning filled with the black point from one of the photos). Bring both scans into photoshop with the "black scan" as a layer on top of the original. Change the blending mode to overlay (also try linear burn and soft light) and adjust the opacity down until the banding disappears. You will probably have to push up the contrast after as this will flatten the look.
Option 3: pick up a new scanner :-)