A direct-injection spark-ignition engine comprising a multi-hole injector adapted to inject a plurality of fuel sprays (Ga, Gb, ---) obliquely downwardly from a peripheral position of a roof wall surface defining a combustion chamber, a spark plug disposed at a center of the combustion chamber-defining roof wall surface, and a concave cavity provided in a central region of a piston crown surface of a piston located in opposed relation to the spark plug, characterized in that: the cavity defines a combustion space having a generally spherical shape with a center at an electrode of the spark plug, when the piston is in a top dead center position, the injector has at least two spray holes consisting of a first spray hole (40a, 140a) adapted to form a first fuel spray (Ga) in such a manner as to, after being injected, directly enter the cavity at a given timing in a later period of a compression stroke, and a second spray hole (40b, 140b) adapted to form a second fuel spray (Gb) in such a manner as to be located below the first fuel spray (Ga), and wherein a timing of fuel injection from the injector during cold engine operation is set to allow the fuel injection to be terminated at a time point when 3/4 of an entire period of a compression stroke has elapsed and set in such a manner as to allow the first fuel spray (Ga) to be turned toward the combustion chamber-defining roof wall surface after entering the cavity, the cavity having a guide sub-surface provided in a part of a region thereof on a far side with respect to the injector, and allow the second fuel spray (Gb) to impinge against a region of the piston crown surface located closer to the injector than the cavity, so as to cause the second fuel spray (Gb) having a lowered penetration force due to the impingement to be pulled toward the cavity by a negative pressure generated in the cavity as a result of passing of the first fuel spray (Ga) therethrough, and held around the spark plug. the cavity defines a combustion space having a generally spherical shape with a center at an electrode of the spark plug, when the piston is in a top dead center position, the injector has at least two spray holes consisting of a first spray hole (40a, 140a) adapted to form a first fuel spray (Ga) in such a manner as to, after being injected, directly enter the cavity at a given timing in a later period of a compression stroke, and a second spray hole (40b, 140b) adapted to form a second fuel spray (Gb) in such a manner as to be located below the first fuel spray (Ga), and wherein a timing of fuel injection from the injector during cold engine operation is set to allow the fuel injection to be terminated at a time point when 3/4 of an entire period of a compression stroke has elapsed and set in such a manner as to allow the first fuel spray (Ga) to be turned toward the combustion chamber-defining roof wall surface after entering the cavity, the cavity having a guide sub-surface provided in a part of a region thereof on a far side with respect to the injector, and allow the second fuel spray (Gb) to impinge against a region of the piston crown surface located closer to the injector than the cavity, so as to cause the second fuel spray (Gb) having a lowered penetration force due to the impingement to be pulled toward the cavity by a negative pressure generated in the cavity as a result of passing of the first fuel spray (Ga) therethrough, and held around the spark plug.