My score is 558 and I own my land and have 50% of building cost of construction loan. Can I get a mortgage for the rest?

I doubt it via traditional sources but I would check with the sources Paul suggested. Good luck!

i do construction loans and i need a 680 fico , with private money investors .. i do have hard money folk, that will loan you the funds please email me at yourloanpartnerforlife@live.com linda

As you can see from others' responses, you are going to have problems with your scenario. Even if you get the construction financing I dont' know of any lender that will provide the permanent mortgage. Consider using some of your cash to improve your credit profile. A better scrore will make the eventual house payment much lower even if you end up borrowing more money. Good luck!