If you notice banding in the image running in the same direction as the sensor moves down the scan bed, the first step is to make sure the photograph lays flat on the glass, especially if you're using a CIS type flatbed scanner. If the photograph is severely curled, you may need to carefully rehumidify and flatten it. Otherwise, weigh it down against the glass with a book.

If that doesn't fix the problem, recalibrate the scanner. This is an option in your scanning software. In VueScan, go to Scanner > Calibrate

If that still doesn't fix the problem, you may have some dust on the scanner sensor.

Another possibility is that the sensor is getting old.

As an alternative to purchasing a new scanner, you could try a black scan:

1. Scan your photograph.
2. Without changing the scan area selection rectangle, scan a sheet of completely black paper.
3. Load both scans into Photoshop with the “black scan” as a layer on top of the original.
4. 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.¹⁾²⁾