Yes you can block a person in facebook!!!!.
Based on facebook “If you block someone, they will not be able to search for you, see your profile, or contact you on Facebook. Any ties you currently have with a person you block will be broken (friendship connections, relationships, etc).”
1. Go to your profile page, on Top right click on the “privacy” link
2. At the bottom of the privacy page you will see the following option. Add the person’s name in that and click “Block”
3. As soon as you click on the “Block” button it will take you to the 3rd page where you will find the option to “Block Person”
4. When you hit that “Block Person” link it will take you back to the Privacy page where you can see the blocked person’s name.
5. You can also remove any person from the block list by clicking on the “(remove)” link.
