ANZ's plan for a 45-metre high skybridge so its bankers could avoid Melbourne's drizzle has drawn criticism from the City of Melbourne.

It's the second sky bridge knocked back recently, with council fighting Crown Casino over plans to build a bridge across Queensbridge Street.

An artist's impress of how the skybridge would look. Credit:Melbourne City Council

ANZ wants to connect its existing headquarters in Docklands with a new 20-level office tower it is building next door.

It has applied to amend its planning permit so it can build an 48-metre-long triangular sky-bridge to connect the buildings at the tenth floor.