Archibald John Norman (May 1, 1954) is a British politician and businessman.

Until 1997, Norman was Chief Executive of Asda, the large supermarket chain, and was credited with turning it around and making it the second largest in the UK. He helped form the think tank Policy Exchange .

Norman was elected as Conservative member of Parliament for Tunbridge Wells in England, in the 1997 general election. Whilst in Parliament he served as a shadow minister from 1999 until 2001, when he returned to the backbenches. He stood down as MP at the May 2005 general election.