Axel Kristjánsson was an Icelandic athlete and merchant. A well known athlete in Iceland, he was part of a group selected to showcase the Icelandic combat sportGlíma at the 1912 Summer Olympics.
Axel had three children with his wife, Hólmfríður. Their son-in-law was the chief of the Icelandic Police, Agnar Kofoed Hansen. Two years after Axel's death, Hólmfríður died from an illness.