A catalytic combustor for a gas turbine comprises catalyst layers arranged in two stages in a direction of gas flow. Fuel supply nozzles are disposed close to and upstream of the downstream catalyst layer. A substantially constant amount of fuel is supplied from the fuel supply nozzles to form pilot flames by the downstream catalyst layer, which are above 1000 degrees C. and below 1500 degrees C. Combustible component having passed through the upstream catalyst layer is burned by the pilot flames.