Can I claim an adult on my income tax?

Two possibilites for being able to claim an adult. First is an adult who lived with you all year, who you supported, who earned less than $3400 (not including Social security).

Second way is if you are supporting a parent (or step parent or in-law) who did not live with you but who you supported and who earned less than $3400 not including SS.

Best thing to do in a situation where you are unsure is to take all your information, including the other adult's income and information in to have your return 'checked' by an experienced tax professional. Some places will do this for free, others charge a minimal fee, well worth it if it keeps you out of IRS trouble.

If you can meet the tests for qualifying relative, yes.

Generally:
Live with you all year.
They made less than $3400.
You provided more than half of their total support.
US citizen or resident of US/Canada or Mexico.
Relationship cannot violate local law.

A boyfriend (for example) will not entitle you to Head of Household status.

See IRS publication 501.

If they live with you ALL year, AND their gross income for the year is under $3400, AND you provide over half of their support for the year, AND your relationship isn't illegal under state or local laws, then you probably can claim them. There are a few more requirements, but those are the main ones.

If the adult is disabled and if you are providing more than 50 percent of their care for the year. This may not be so if that person has income.