You may be eligible if:
You have been a permanent resident for at least 5 years and meet all other eligibility requirements; or
You have been a permanent resident for 3 years or more and meet all eligibility requirements; or
You have qualifying service in the U.S. armed forces and meet all other eligibility requirements.
Note also that your child may qualify for naturalization if you are a U.S. citizen, the child was born outside the U.S., the child is currently residing outside the U.S., and all other eligibility requirements are met. And, in come cases you may already be a U.S. citizen and not need to apply for naturalization if your biological or adoptive parent(s) became a U.S. citizen before you reached the age of 18.
Be sure to see our other citizenship and naturalization related pages:
The Naturalization Process
Brief Naturalization Guide
Naturalization Test Help
Naturalization for Armed Forces