<p>A direct fuel-injection engine includes a piston, a cavity recessed in a central part of a top face of the piston, and a fuel injector. At a main injection collision point of a fuel-injection axis when main injection is performed while the piston is near top dead center, a main injection collision angle formed between its tangent and the fuel-injection axis is set at an obtuse angle. Fuel colliding with the main injection collision point is deflected towards a cavity open end side. At a secondary injection collision point of the fuel-injection axis when performing secondary injection with the piston is further from top dead center, a secondary injection collision angle formed between its tangent and the fuel-injection axis is set at one of a right angle and an acute angle. Fuel colliding with the secondary injection collision point is deflected primarily in the circumferential direction of the cavity.</p>