Illustrator is a vector image editor - so banding in gradients is kind of inherent in this type of software, and ultimately there is no way to avoid it fully. The gradients are basically made of vector shapes, each filled with steps of colour to give the illusion of a gradient.
It might be possible instead to make a blend of two shapes, with more steps than the gradient tool allows for. But honestly, it's a lot of messing around.
You might be better to use Photoshop to create a raster gradient instead.
Anway here's an example of a 400 step blend made in Illustrator for comparison to your original. Is it any better? Hmmm . . . probably not much.
One way to reduce the banding effect in gradients is to apply subtle noise. This works better in Photoshop, but it does work pretty well in Illustrator as well. Select the object, then select Object>Artistic>Film Grain... Set it as follows:
Highlight Area: 0
See image for before (above) and after (below) It's not a perfect solution, but Illustrator needs to upgrade their own rendering engine for a better solution.