The invention relates to a shape of a combustion chamber for a direct-injection diesel engine, in which a mixture in, particularly, an expansion stroke is promoted by optimally designing the shape of the combustion chamber, and further, the compatibility between PM reduction and NOx reduction can be achieved by improving a retardation limit and speeding up combustion at a high EGR. The inside of a combustion chamber 12 formed at a top of a piston is formed in such a manner that a vertically cross-sectional shape passing a center axis O2 inside of the combustion chamber is symmetric with respect to the center axis. Furthermore, an opening 18 at an upper end of the combustion chamber 12 is formed into a substantially polygonal shape in combination of round portions 21 and straight portions 22.