Controller for direct injection engine

When an engine is at starting or at cold state, a closing time of an exhaust valve is set before an intake top dead center to close the exhaust valve early. An exhaust residual gas is compressed by a cylinder to raise an inner cylinder temperature. A pre-fuel injection is performed from a time of closing the exhaust valve to a time of the intake top dead center in such a manner that the pre-injected fuel is combusted to raise the inner cylinder temperature. This increase in temperature expedites an atomization of fuel injected at a main fuel injection. A wet amount of fuel is reduced and HC emission is also reduced.