Can i claim head of household if my son lives with me but i am not claiming him as a dependent?

Are you the custodial parent?  Do you have an agreement with the other parent to allow the other parent to claim them--due to divorce or that you live apart and share custody?  Did one of you sign a Form 8332?

If there is a signed 8332 then the custodial parent retains the right to file as Head of Household, get earned income credit and the childcare credit.  The non-custodial parent gets the child tax credit for children under the age of 18.

As far as the IRS is concerned, the custodial parent is the one with whom the child spent the most nights during the tax year--at least 183 nights.

If you are a non-married couple who live together then only one of you can claim the child(ren) and the one not claiming the child does not enter anything at all on their tax return about the child. 

Head of Household

You may be able to file as head of household if you meet all the following requirements.

1. You are unmarried or considered unmarried on the last day of the year. See Marital Status, earlier, and Considered Unmarried, later.
2. You paid more than half the cost of keeping up a home for the year.
3. A qualifying person lived with you in the home for more than half the year (except for temporary absences, such as school).

Considered Unmarried

To qualify for head of household status, you must be either unmarried or considered unmarried on the last day of the year. You are considered unmarried on the last day of the tax year if you meet all the following tests.

1. You file a separate return. A separate return includes a return claiming married filing separately, single, or head of household filing status.
2. You paid more than half the cost of keeping up your home for the tax year.
3. Your spouse didn't live in your home during the last 6 months of the tax year. Your spouse is considered to live in your home even if your spouse is temporarily absent due to special circumstances. See Temporary absences, later.
4. Your home was the main home of your child, stepchild, or foster child for more than half the year. (See Home of qualifying person, later, for rules applying to a child's birth, death, or temporary absence during the year.)
5. You must be able to claim the child as a dependent. However, you meet this test if you can't claim the child as a dependent only because the noncustodial parent can claim the child using the rules described later in Children of divorced or separated parents (or parents who live apart) under Qualifying Child or in Support Test for Children of Divorced or Separated Parents (or Parents Who Live Apart) under Qualifying Relative. The general rules for claiming a child as a dependent are explained later under Dependents.