State Route 613 is a secondary state highway

State highway

State highway, state road or state route can refer to one of three related concepts, two of them related to a state or provincial government in a country that is divided into states or provinces :#A...

 in the southwest part of the U.S. state

U.S. state

A U.S. state is any one of the 50 federated states of the United States of America that share sovereignty with the federal government. Because of this shared sovereignty, an American is a citizen both of the federal entity and of his or her state of domicile. Four states use the official title of...

 of Virginia

Virginia

The Commonwealth of Virginia , is a U.S. state on the Atlantic Coast of the Southern United States. Virginia is nicknamed the "Old Dominion" and sometimes the "Mother of Presidents" after the eight U.S. presidents born there...

, running northeasterly from State Route 71

State Route 71 (Virginia)

State Route 71 is a primary state highway in the southwest part of the U.S. state of Virginia. It runs from Gate City northeast to Lebanon, mostly through river valleys. Despite running more east–west than north–south, it is signed north–south; it parallels the similarly-oriented...

 north of Gate City to U.S. Route 58 Alternate at Bolton. Except for the northeasternmost three miles (5 km), SR 613 runs through the valley formed by Big Moccasin Creek.

Part of the road in Russell County, southwest from US 58 Alternate (then State Route 110), was added to the state highway system in 1931 (4.12 mi/6.63 km) and 1932 (2.24 mi/3.60 km) as State Route 134. It became State Route 74 in the 1933 renumbering, and was transferred to the secondary system in 1942.