In a direct fuel-injection engine equipped with a pentroof-shaped piston, cross-sectional shapes containing a piston central axis (Lp) of a cavity recessed in a central part of the piston having a top face with the height varying in the circumferential direction are set so as to be basically identical at each position in the circumferential direction (see broken line). Since the sizes of the cross-sectional shapes of the cavity thereby become different in a region further on the piston central axis (Lp) side than intersection points (e1, d1) in the vicinity of a fuel injection point (Oinj), in order to compensate for this, by correcting in a cross section that is away from the piston pin direction the cross-sectional shape of the broken line into the cross-sectional shape of a solid line so that it enlarges, the size of the cross-sectional shape at each position of the circumferential direction of the cavity is thereby made more uniform, thus making the conditions in which fuel and air are mixed uniform and improving the engine output and reducing harmful exhaust materials.