An ignition control apparatus for igniting an internal combustion engine which at least comprises: a dc power supply; a step-up circuit which steps up a power supply voltage at said dc power supply; an ignition coil which develops a high secondary voltage at a secondary winding by an increase or a decrease in current flowing in the primary winding connected to said step-up circuit; an ignition switching device which switches between supply and cutoff of current to said primary winding according to an ignition signal (IGt) outputted as a function of a running condition of the internal combustion engine; a spark plug which is connected to said secondary winding and produces a spark discharge upon application of secondary voltage from said secondary winding, wherein it also comprises an auxiliary power supply which additionally performs discharge from said the step-up circuit to a junction between the primary winding of the ignition coil and the ignition switching device and then stop the discharge, thereby increasing current through said secondary winding in a discharge period of time after start of discharge from said spark plug made by opening or closing said ignition switching device, and wherein said auxiliary power supply is equipped with an auxiliary switching device which switches between discharge from said auxiliary power supply and stop of the discharge, wherein the ignition control apparatus comprises an auxiliary switching device driving circuit (421, 421a, 421b) which opens or closes the auxiliary switching device, characterized in that the ignition control apparatus further comprises a frequency calculating portion (210, 210a, 210b) which increases in said discharge period of time between start of discharge and end of the discharge the drive pulse frequency toward the end of the discharge and which increases or decreases a rate of increase in drive pulse frequency for said auxiliary switching device as a function of at least two engine parameters (EPr) indicative of a running condition of the internal combustion engine, and in that the at least two engine parameters (EPr) comprises an engine speed (Ne) and an intake pressure, and the rate of increase in drive pulse frequency is increased or decreased as a function of the engine speed (Ne) and an intake pressure such that, when the engine speed (Ne) and the intake pressure are both decreased, a rate of increase in drive pulse frequency is decreased while the pulse length is kept constant, and such that, when the engine speed (Ne) and the intake pressure PIN are both increased, the rate of increase in drive pulse frequency is increased while the pulse length is kept constant. a dc power supply; a step-up circuit which steps up a power supply voltage at said dc power supply; an ignition coil which develops a high secondary voltage at a secondary winding by an increase or a decrease in current flowing in the primary winding connected to said step-up circuit; an ignition switching device which switches between supply and cutoff of current to said primary winding according to an ignition signal (IGt) outputted as a function of a running condition of the internal combustion engine; a spark plug which is connected to said secondary winding and produces a spark discharge upon application of secondary voltage from said secondary winding, wherein it also comprises an auxiliary power supply which additionally performs discharge from said the step-up circuit to a junction between the primary winding of the ignition coil and the ignition switching device and then stop the discharge, thereby increasing current through said secondary winding in a discharge period of time after start of discharge from said spark plug made by opening or closing said ignition switching device, and wherein said auxiliary power supply is equipped with an auxiliary switching device which switches between discharge from said auxiliary power supply and stop of the discharge, wherein the ignition control apparatus comprises an auxiliary switching device driving circuit (421, 421a, 421b) which opens or closes the auxiliary switching device, characterized in that the ignition control apparatus further comprises a frequency calculating portion (210, 210a, 210b) which increases in said discharge period of time between start of discharge and end of the discharge the drive pulse frequency toward the end of the discharge and which increases or decreases a rate of increase in drive pulse frequency for said auxiliary switching device as a function of at least two engine parameters (EPr) indicative of a running condition of the internal combustion engine, and in that the at least two engine parameters (EPr) comprises an engine speed (Ne) and an intake pressure, and the rate of increase in drive pulse frequency is increased or decreased as a function of the engine speed (Ne) and an intake pressure such that, when the engine speed (Ne) and the intake pressure are both decreased, a rate of increase in drive pulse frequency is decreased while the pulse length is kept constant, and such that, when the engine speed (Ne) and the intake pressure PIN are both increased, the rate of increase in drive pulse frequency is increased while the pulse length is kept constant.