PURPOSE: To restrict an excess air ratio, improve a thermal efficiency and restrict a generation of soot to a minimum by a method wherein oxidation catalyst decreasing substantially an ignition temperature of fuel is fixed to a wall surface of a combustion chamber of an internal-combustion engine.

CONSTITUTION: A part near a combustion chamber of internal-combustion engine is composed of an eddy flow chamber 1, fuel injection valve 3 and glow plug 4 etc. An oxidation catalyst is fixed to a catalyst surface 7a of a piston 7, a catalyst surface 6a of a cylinder head 6, an inner wall surface 10a of a sub- chamber 10 and a wall surface of a communication hole 5 etc. In the combustion chamber, both a flame combustion and a catalyst combustion are continued to proceed. In this way, the combustion speed of the flame is promoted and then a thermal efficiency can be improved.