I suggest you do the tests again for HBsAg, Anti HBs, Anti HBc to see if it is really false positive. If it is, vaccine is the best way to protect yourself against HBV infection, and if it is not false positive, then, you may belong to the small percentage of people with an ISOLATED Anti HBc (here is a link about it):
http://depts.washington.edu/hepstudy/hepB/clindx/core/discussion.html
But let's not jump into conclusions ahead, do the tests again, and then see whether you fall into that group or not.
Good luck and good health
Thank you for your reply.
6 months ago I had a blood test where HBsAg and HBsAb were negative. I didn't test the HBcAb then. The technician told me that probably I am false positive cause It is very close to 0.8
My test results are the same as yours, so try reading my previous posts because I got some pretty useful answers from Stefano. It might answer your questions.
Have you ever had an HBV infection (acute or chronic), or is this your first blood test about HBV?