A cylinder direct injection type internal combustion engine, including a fuel injection device configured to directly inject a first octane-value fuel and a second octane-value fuel into a combustion chamber. The second octane-value fuel has an octane value larger than an octane value of the first octane-value fuel. A controller is programmed to perform a first operation mode. In the first operation mode, the first octane-value fuel is injected from the fuel injection device, and the second octane-value fuel is injected from the fuel injection device toward an ignition flame formed by self-ignition combustion of the first octane-value fuel, so as to cause flame propagation and combustion of the second octane-value fuel.