The contract forTunny's construction was awarded on 25 June 1968 and her keel was laid down on 22 May 1970 at Pascagoula, Mississippi, by the Ingalls Shipbuilding Division of Litton Industries.

She was launched on 10 June 1972, sponsored by Mrs. Lola Aiken, and commissioned on 26 January 1974 at her home port, Charleston, South Carolina.

Tunny remained at Charleston until March 1974, when she moved to Groton, Connecticut, for two weeks of in-port training at the submarine base.

Following refit and upkeep alongside a submarine tender in June and early July 1975 at Santo Stefano, Sardinia, Italy, Tunny rejoined the Sixth Fleet as a unit of Task Force 69 and resumed antisubmarine warfare training.

February 1976 brought inspections and examinations and, in March 1976, she participated in two special operations designed to help develop and evaluate submarine tactics.

In October 1976, she returned to sea for antisubmarine warfare training operations punctuated periodically with a visit to Naples, Italy, or upkeep at Santo Stefano.

Tunny was assigned to Submarine Squadron 1, and devoted the remainder of 1978 to operations in the Hawaiian Islands in preparation for a 1979 deployment to the Western Pacific.

She was a guest of the Royal Australian Navy when she visited HMAS Stirling, the administrative center of the Royal Australian Navy's main naval base on the west coast of Australia, located on Garden Island just off the coast of Western Australia near the city of Perth, and Tunny's crew participated in the ANZAC Day Parade in April 1979.