A driving apparatus in a printing press includes a plate cylinder driven by a printing press motor, an inking device drive-coupled to the plate cylinder, and a driving connecting/disconnecting mechanism. The mechanism connects and disconnects transmission of driving from the plate cylinder to the inking device, and includes first and second gears which are engageable with each other, supported rotatably, and constantly drive-coupled to one and the remaining one, respectively, of the plate cylinder and inking device. The second gear has a second engaging portion engageable with a plurality of first engaging portions of the first gear which have the same shape and are equidistantly arranged in a rotational direction of the first gear. When the first and second engaging portions engage, the plate cylinder and inking device are drive-coupled; when they are disengaged, they are disconnected. The number of first engaging portions is set on the basis of a value related to the first gear, so that when the plate cylinder reaches a phase identical to that where the first and second engaging portions disengage, the first and second engaging portions can engage regardless of a driving connection ratio of one of the plate cylinder and inking device to the first gear.