Nielsen graduated from Little Sioux High School and became a farmer.
He was affiliated with the Democratic Party and had served as Sherman Township trustee and president of the Blencoe school board before being elected to the Iowa House of Representatives.
After stepping down from the state house, Nielsen remained active in politics as mayor of Blencoe.
[1] Nielsen married Irene Miller Perry on 22 July 1922.
Harry Nielsen died on 8 August 1981 at Burgess Memorial Hospital in Onawa.