A gasoline direct-injection engine includes a cavity provided in a top portion of a piston and constituting a portion of a combustion chamber defined between a cylinder head and the top portion of the piston, a fuel injection valve mounted in the cylinder head for injecting gasoline directly into the combustion chamber, and a spark plug also mounted in the cylinder head to face the combustion chamber. In this gasoline direct-injection engine, the fuel injection valve facing a substantially central portion of a ceiling surface of the combustion chamber is mounted in the cylinder head to have an axis substantially parallel to an axis of the piston, and the cavity provided in the top portion of the piston and disposed below the fuel injection valve and the spark plug is defined so that it is deeper in an area corresponding to the spark plug than in an area corresponding to the fuel injection valve. Thus, it is possible to achieve a stable lean laminar burn in wide ranges of rotational speed and load of the engine, thereby providing an improvement in fuel consumption and an enhancement in nature of an exhaust gas.