Annear was born in Exeter, Devon, and studied at Exeter College of Art in painting and printmaking. After obtaining a B Ed at Rolle College, Exmouth, Devon he lectured and became Director of Ryder's Gallery, Dartington College of Art, Devon. In 1988 he became a member of the Penwith Society of Artists, and the following year a member of the Newlyn Society of Artists, for which he later served on the Council of Management of NAG and a committee member of the NSA.
His solo exhibitions include shows in Cornwall, Germany, France, most recently at the New Millennium Gallery, St Ives (2007), and his group exhibitions many all over the UK and Europe. In 1991-92 he worked in Worpswede, Germany with the support of a DAAD scholarship and other awards.
A modernist in style, his work is said to show cubist influences, and he has stated that he finds the term 'abstract' too confining (Catalogue intro: New Millennium Gallery). He now lives and works on the Lizard Peninsula in a converted chapel, with his wife, the artist Judy BUXTON..