The Ohio congressman said Cheney manipulated and fabricated intelligence on weapons of mass destruction to justify the Iraq war.
Kucinich earlier had called off his planned filing because Cheney was taken to a doctor for tests on a blood clot in his leg. He went ahead after Cheney criticized Democrats for pushing ahead with anti-war legislation in Congress.
Kucinich said it was important to introduce the legislation, "because the threat of war against Iran is very real."
"This vice president cannot be permitted to continue to violate both the U.S. Constitution and the U.N. Charter," he said.
House speaker Rep. Nancy Pelosi has said impeachment is off the table.