(CNN) -- The Brady Center to Prevent Gun Violence filed a federal lawsuit Thursday against Nelson, Georgia, a small town north of Atlanta.
Officials in Nelson passed an ordinance in April requiring every head of household to have a gun and ammunition. Nelson's five-member town council unanimously approved the law, which says violators could be fined up to $1,000.
The Brady Center, the legal branch of a long-running Washington-based organization of gun control advocates, says that Nelson's new law in unconstitutional.
The ordinance exempts people who "suffer from a physical or mental disability," felons, "paupers" or people who "conscientiously oppose maintaining firearms as a result of beliefs or religious doctrine."
The suit says the law violates the First Amendment to the Constitution because requiring people to purchase a firearm when they don't want to own one violates their freedom of speech and their "freedom to act or not to act." The law violates the 14th Amendment because it creates two classes of individuals: heads of households and non-heads of households, the suit says.
The suit also says the law violates the Second Amendment, because that amendment does not require, or permit the government to require, owning a firearm.
And there are residents of Nelson who have suffered economically because of the law, the suit says. It says longtime resident Harold Lamar Kellett was "forced" to purchase a handgun and ammunition, which cost him nearly $700 -- a financial burden he should not have to bear.
The ordinance "has stripped Mr. Kellett of his right to determine how best to protect his home and compelled him to take action and communicate with the public in a manner he would not otherwise have done," according to the suit.
Nelson's law was modeled on a similar law in nearby Kennesaw, Georgia, a measure that has been on the books since 1982.
Nelson is home to about 1,300 people.