A capacitor-discharge-type ignition device for an internal combustion engine, comprising: an exciter coil that generates an AC voltage having a positive half-wave voltage and first and second negative half-wave voltages present before and after the positive half-wave voltage synchronously with rotation of the engine; ignition-position detection time data calculating means that arithmetically operates as ignition position detection time data, the time period that is required for the engine to rotate from the generating position of the second negative half-wave voltage to an ignition position suitable in starting period, at the rotational speed of the engine that is obtained from time period from generation of the first negative half-wave voltage to the generation of the second negative half-wave voltage, and from an angle between the generating position of the first negative half-wave voltage and that of the second negative half-wave voltage, wherein a crank angle position when the measurement of the arithmetically operated ignition position detection time data is completed is determined as an ignition position at a low speed operation of the engine.