Nope ... Barter is the only other option to having currency. It doesn't work on a large scale. And currency requires banking, to work on a large scale.
Why do we actually need the banking system? Could society and the world continue peacefully without it?
There'd have to be some kind of system. Barter is too primitive a method. Perhaps something like the Hawalah system would work, but that's just another form of banking when you think about it.