You can't delete a contact in Facebook. However, there's an "unfriend" button, which is equivalent to "delete" a contact. Once you unfriend that contact,he or she would be removed from your contact list.

To unfriend your contact, go to friends (as shown on the red arrow)


Click "All Friends" to see the name of the contact you want to remove.


Click the name of the contact you want to remove and click "Unfriend..(the person's name)..."