Since I was taxed 20% from my 401k withdrawal, will I be taxed another 10% now that I'll be filing for taxes?

[DoninGA]

If you made an early withdrawal from the 401(k) there will be a 10% early distribution penalty assessed on your federal tax return, Form 1040.  It will be entered as a tax liability.

[PaulaM]

If you are under 59.5, then there is a 10% penalty that will be added to your taxes owed when you complete your return. Please see this article for reference. 

The 20% withheld from your 401k may or may not cover your total tax liability. It functions much like the federal tax withheld on a paycheck would.