The lawsuit, filed in U.S. District Court in Kansas City, asks a judge to declare the ordinance and its enforcement unconstitutional.
The St. Joseph city attorney's office did not immediately return a call seeking comment today.
The church believes that U.S. troop deaths are punishment for the nation's tolerance of homosexuality.
Phelps-Roper is pursuing a similar suit against the state of Missouri. A three-judge panel of the 8th U.S. Circuit Court of Appeals ruled in October that church members could picket soldiers' funerals in Missouri.