He was trained clerk at the District office in Aarhus, and in 1824 trained as a portrait painter at the Royal Danish Academy of Fine Arts. Møller primarily painted portraits. Møller painted Hans Christian Andersen.
He served in 1844 as daguerreotypist in Elsinore, and in 1850 as a photographer, both in Elsinore and Copenhagen.
He was the father of Johan Christian Møller, who became Head of the Army Medical Corps and in 1895 served as Surgeon General. He is buried in Assistants Cemetery.