People aged 18 are considered adults "for almost all purposes and certainly for the purposes of the exercise of fundamental constitutional rights", the lawsuit says.
The complaint says the law violates the second amendment of the US constitution, which protects the right to bear arms.
It also argues the bill breaches the 14th amendment's equal protection clause by banning law-abiding citizens between 18-21 from buying guns.
"Preventing a responsible 20-year-old from purchasing the best tool for self-defence will not stop a deranged criminal intent on committing a crime," the lobby group said.
"Females between the ages of 18 and 21 pose a relatively slight risk of perpetrating a school shooting... or, for that matter, a violent crime of any kind," says the lawsuit.
It also points out that men of 21-24, just outside the new age limit, account for more violent crime arrests than men aged 18-21.