He was elected to the Parliament of Norway from Hedmark in 2005 and re-elected in 2009 and 2013. Vedum started out in the Standing Committee on Local Government and Public Administration, then changed to the Standing Committee on Health and Care Services in 2008. In October 2008 he became deputy leader here, and also Second Deputy President of the Odelsting as well as party whip. He was also a member of the Electoral Committee from 2005 to 2012, and from 2009 to 2012 the Standing Committee on Foreign Affairs and Defence and the Enlarged Committee on Foreign Affairs and Defence.