A direct-injection internal combustion engine includes a variable-exhaust-valve control device for controlling value timing of a variable exhaust valve through which the combustion chamber of an engine cylinder communicates with an exhaust path. The variable-exhaust-value control device retards the opening timing of the variable exhaust value to a retard side when the fuel is injected during a compression stroke or an expansion stroke while the direct-injection internal combustion engine is operating in a cold-start state.