A control apparatus for a compression self-igniting internal combustion engine including a supercharger of a variable capacity type having a variable capacity mechanism , the control apparatus comprising a control means that controls the variable capacity mechanism such that an actual ignition delay period (Dest) of fuel injected into a cylinder from a fuel injection valve is brought close to a target ignition delay period (Dtrg), the variable capacity mechanism being a variable nozzle vane mechanism that adjusts an opening degree of a plurality of nozzle vanes that can vary a flow path area of an exhaust gas flow path inside the supercharger , characterized in that the control means being configured to calculate a proportional term (Pvnp) and an integral term (Pvni), both for obtaining a control value for correcting the opening degree of the nozzle vanes , based on a difference (Ddif) between ignition delay periods obtained by subtracting the actual ignition delay period (Dest) from the target ignition delay period (Dtrg), calculate a sum of the proportional term (Pvnp) and the integral term (Pvni) as a nozzle-vane-opening-degree control value (PVN), control the opening degree of the nozzle vanes based on the nozzle-vane-opening-degree control value (PVN) thus calculated, and increase the opening degree of the nozzle vanes such that the larger the difference (Ddif), the longer the actual ignition delay period (Dest) of fuel, and the control means being configured such that, in a case of controlling an ignition delay period by adjustment of the opening degree of the nozzle vanes in an opening degree region where the opening degree is relatively large, an amount of nozzle vane opening degree change relative to an amount of unit ignition delay period change is set so as to be larger than in a case of controlling the ignition delay period by adjustment of the opening degree of the nozzle vanes in an opening degree region where the opening degree is smaller than in the former opening degree region. the control apparatus comprising a control means that controls the variable capacity mechanism such that an actual ignition delay period (Dest) of fuel injected into a cylinder from a fuel injection valve is brought close to a target ignition delay period (Dtrg), the variable capacity mechanism being a variable nozzle vane mechanism that adjusts an opening degree of a plurality of nozzle vanes that can vary a flow path area of an exhaust gas flow path inside the supercharger , characterized in that the control means being configured to calculate a proportional term (Pvnp) and an integral term (Pvni), both for obtaining a control value for correcting the opening degree of the nozzle vanes , based on a difference (Ddif) between ignition delay periods obtained by subtracting the actual ignition delay period (Dest) from the target ignition delay period (Dtrg), calculate a sum of the proportional term (Pvnp) and the integral term (Pvni) as a nozzle-vane-opening-degree control value (PVN), control the opening degree of the nozzle vanes based on the nozzle-vane-opening-degree control value (PVN) thus calculated, and increase the opening degree of the nozzle vanes such that the larger the difference (Ddif), the longer the actual ignition delay period (Dest) of fuel, and the control means being configured such that, in a case of controlling an ignition delay period by adjustment of the opening degree of the nozzle vanes in an opening degree region where the opening degree is relatively large, an amount of nozzle vane opening degree change relative to an amount of unit ignition delay period change is set so as to be larger than in a case of controlling the ignition delay period by adjustment of the opening degree of the nozzle vanes in an opening degree region where the opening degree is smaller than in the former opening degree region. <EOS>