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.

Read more: Do You Qualify for US Citizenship Thorough Naturalization?

Basic Facts About Naturalization Eligibility © 2010-2011 Peter J. Loughlin, Esq. and Thomas W. Goldman, Esq.
Age Requirement for Naturalization
In order to apply for naturalization an applicant must first be a lawfully admitted permanent resident of the United States of at least 18 years of age.

Good Moral Character Requirement
All applicants for naturalization must be of good moral character. Certain crimes and bad acts, even though not resulting in a criminal conviction, may make one ineligible to naturalize for lack of good moral character. In addition some crimes or acts may be sufficient cause to deny the application and place the applicant in proceedings to be removed from the United States. It is highly advisable to contact an immigration attorney if you have committed (even if not arrested) or been convicted any crime or bad act before filing for naturalization. More Information About Good Moral Character

Continual Residence Requirement

Read more: Naturalization Guide