To provide high definition printing by increasing the amount of ink delivered from a gravure cylinder and preventing transfer failures, in a gravure-offset printing machine.

An impression cylinder 6 is separated from a blanket cylinder 4, when ink is being delivered to a blanket cylinder 4 from the gravure cylinder 1 with recesses to be filled with ink 2 formed on the circumferential surface thereof. While, the gravure cylinder 1 is separated from the blanket cylinder 4, when ink is being transferred from the blanket cylinder 4 to a matter 7 to be printed. Furthermore, the rotation speed V2 of the blanket cylinder 4 and the gravure cylinder 1, when ink is delivered to the blanket cylinder 4, is relatively slower than the rotation speed of the blanket cylinder 4 and the impression cylinder 6 when ink is being transferred to the matter to be printed 7.