A catalyst carrier, an electrode catalyst, an electrode including the catalyst, a membrane electrode assembly including the electrode, and a fuel cell including the membrane electrode assembly. The catalyst carrier includes a carbon material having a chain structure including a chain of carbon particles and an alumina-carbon composite particle in which a carbon particle encloses an alumina particle, the alumina-carbon composite particle is contained in the carbon material, and the catalyst carrier has a BET specific surface area of 450 to 1100 m2/g.