a control device for a multi - cylinder engine comprises , in addition to a sensor 11 for detecting reference rotational positions of the crank shaft 1 , an ionization current detector 41 for detecting the ionization current across a spark plug 33 of a cylinder . from the output of the sensor 11 , the microcomputer 40 discriminates the group of cylinders which are in the compression and the exhaust stroke . for a short period after the start of the engine , the group of cylinders in the compression and the exhaust stroke are ignited simultaneously . during this short period , the cylinder in the compression stroke is discriminated from the group of cylinders in the compression and the exhaust stroke , on the basis of the output of the ionization current detector 41 , and the number of succesive discriminations of the cylinder in the compression stroke is counted . when this number reaches a predetermined number n , a flag f is set , such that only the cylinder in the compression stroke is supplied with the ignition current thereafter .