Can you claim head of household and claim your boyfriend as a dependent?

Unless your boyfriend is a relative listed in Table 4 on page 8 of Publication 501

http://www.irs.gov/pub/irs-pdf/p501.pdf

or you also happened to have another qualifying relative for whom you kept up a home, then you cannot file as Head of Household.

If your boyfriend lived with you as part of your household, you may be able to claim him as a dependent. Please refer to Table 5 on page 11 of Publication 501:

http://www.irs.gov/pub/irs-pdf/p501.pdf

Note that a person who lived with you can be a "qualifying relative" even if you are not related to each other.

I realize this is very confusing. Your boyfriend could be a "qualifying relative" for purposes of claiming a dependent exemption, but not a "qualifying person" for purposes of claiming Head of Household status.