In an engine igniting coil device of the open-magnetic-circuit type that has a bobbin having a hollow axis having a circular section in which a rod-shape core is inserted, the core is formed of a plurality of iron plates having different widths and laminated to have a substantially circular section and the thus formed core is splitted in the direction perpendicular to the lamination into a plurality of parts in order to increase a space factor of the core in the bobbin's hollow axis having a circular section and to easily accommodate the core in the bobbin's hollow axis having a circular section assuring a high space factor of the core therein and reducing eddy-current core-loss to improve an output factor of a secondary voltage.