Steingímur has a long career as an artist and has been an active participant on the Icelandic art scene throughout his career. He was one of the founders of Gallery Sudurgata 7 and a founding member of the Living Art Museum. Steingrimur represented Iceland at the Venice Biennale in 2007 and won the Visual Arts Awards for the show a year later.

Steingrimur works in various media, and his work is often a mixture of text and drawings. Serious questions and criticisms about society is often his subject matter and in his work he creates a connection between the irrational and rational. Elements of popular culture, folklore, politics, philosophy and everyday life connecting art with him.