NOVELTY - Oxygen-reduction catalyst comprises composite particles comprising carbon structure, particles containing group (IV) metal element, carbon, nitrogen and oxygen. The particles containing group (IV) metal element are dispersed in the carbon structure. The mass-reduction level (a) and mass-reduction level (b) of composite particles are 15% or less and 25-70%, respectively, measured by thermogravimetry/differential thermal analysis-simultaneous measurement at gas flow rate of 0.2 L/minute.    USE - Oxygen-reduction catalyst is used in catalyst layer of electrode e.g. cathode and anode of membrane-electrode assembly for fuel cell (all claimed) e.g. polymer-electrolyte fuel cell. Uses include but are not limited to fluorescent lamp, interior lighting, signal apparatus, motor vehicle, mobile telephone, cosmetic equipment, portable information terminal, cooler, cardiac pacemaker, Peltier device, etc.    ADVANTAGE - The fuel cell provided using oxygen-reduction catalyst has high energy conversion efficiency, and excellent stability and start-stop durability.    DETAILED DESCRIPTION - Oxygen-reduction catalyst comprises composite particles comprising carbon structure, particles containing group (IV) metal element, carbon, nitrogen and oxygen, in which particles containing group (IV) metal element are dispersed in the carbon structure. The mass-reduction level (a) and mass-reduction level (b) of composite particles are 15% or less and 25-70%, respectively, measured by thermogravimetry/differential thermal analysis-simultaneous measurement at gas flow rate of 0.2 L/minute, by heating to 30-100 degrees C at heating rate of 10 degrees C/minute, maintaining at 100 degrees C for 30 minutes and further heating to 100-800 degrees C at heating rate of 10 degrees C/minute. The mass-reduction level (a) is product of ratio of mass which reduces at 300-500 degrees C to mass at 300 degrees C. The mass-reduction level (b) is product of ratio of mass which reduces at 300-800 degrees C to mass at 300 degrees C. INDEPENDENT CLAIMS are included for the following:    (1) membrane-electrode assembly, which consists of polymer electrolyte membrane provided in between cathode and anode; and    (2) manufacture of oxygen-reduction catalyst, which involves oxidizing a portion of carbon contained in carbon structure of composite particles precursor using oxidizing gas containing oxygen.