Michael Brown, 18, was shot dead by Ferguson police in August 2014.
The wrongful-death suit seeks a minimum of $75,000 compensation.
The shooting of the unarmed Michael Brown by white police officer Darren Wilson in Missouri became a national cause and sparked protests, some violent.
The shooting was reviewed by a grand jury, which decided in November not to charge Darren Wilson.
However, Michael Brown’s parents say they have new forensic evidence that raises questions about the police version of events.
“The narrative of the law enforcement all across the country for shooting unarmed people of color is the same: That they had no other choice,” attorney Benjamin Crump said.
“But time and time again, the objective evidence contradicts the standard police narrative.”
Along with seeking punitive damages from the City of Ferguson, the suit also calls for a court order prohibiting the use of police techniques “that demean, disregard, or under-serve its African-American population”.
A St Louis County grand jury and the Department of Justice had declined to prosecute Darren Wilson, who resigned in November. Civil cases generally require a lower standard of proof than criminal cases.
This is not the only current civil case involving the police killing of an unarmed black man. In New York, the family of Eric Garner is seeking $75 million in damages.
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