In a heat-insulating swirl chamber engine of this invention, a fuel is injected subsidiarily from subsidiary nozzles (2) along the inner wall surfaces (16) of swirl chambers (4) of a heat-insulating structure from the second half of an intake stroke to the first half of a compression stroke, so that a lean mixture formed in the swirl chambers (4) does not diffuse into cylinders (14), deterioration of hydrocarbon components can be prevented and moreover, since the fuel comes into contact with the wall surfaces (16) of the swirl chamber, heat energy can be recovered from the wall surfaces (16). Next, the fuel is mainly injected from main nozzles (3) into the swirl chambers (4) from the second half of the compression stroke to the first half of an expansion stroke, so that the inside of the swirl chambers (4) becomes fuel-rich due to the lean mixture formed in advance in the swirl chambers (4) and the fuel by the main injection, combustion is effected in the fuel-rich state to restrict the generation of NOx and moreover, cycle efficiency can be improved because the main combustion period is shortened.