How to prevent the login block to be shown twice?
Follow the steps, Using which can solve your problem.


Go to Blocks under structure admin menu.
You will find user login block in Header section. 
If you have added your custom login block then there is no need to have default login widget in header. So change it to null.
If you have default login then just check to put it in appropriate block.


This are the two cases according to your question description.Answer back if not solved.

Please do mention some more description if this solution won't work.