The £38m three-storey building to be known as the Magnet will feature interactive exhibits, a planetarium and laboratory.
The charity behind the project, Science Oxford, forecasts that the centre could draw in 150,000 visitors each year.
If permission is granted, construction is expected to start in early 2015.
It will replace the 1960s building, formerly Macclesfield House, and the function of the Registry Office, which will be relocated to another building owned and operated by Oxfordshire County Council.