To provide a driving method for an offset rotary press with which the number of sheets required for trial printing due to less density caused by an insufficient ink supply on a surface of each roller at the beginning of printing is decreased.

A plate cylinder equipped with a press plate, a blanket cylinder which make a printing on a web by making ink transfer from the plate cylinder, an ink fountain having a plurality of blades and an ink roller are provided. An inking apparatus which draws ink from the ink fountain by making a predetermined opening between each blade and the ink roller, and a printing unit equipped with an ink transmission roll group consisting of a plurality of rubber rollers and metal rollers which are set between the inking apparatus and the plate cylinder and transmit to the plate cylinder the ink supplied by the inking apparatus are also provided. In the driving method of the offset rotary press thus provided, when starting printing, the ink roller is speeded up beforehand by a predetermined time than in an ordinary operation, and after a predetermined time passed, speeded down to the ordinary operation.