To reduce the broke by shortening the time required for cleaning a blanket cylinder and the time attributable to a cleaning operation, in an offset rotary press.

This blanket cleaning method comprises the following processes: a primary cleaning process to suspend the supply of ink and damping water to a plate cylinder and transfer the ink from the surface of a cylinder to a web, in such a state that the web running at almost the same velocity as during printing is brought into contact with the cylinder surface of the blanket cylinder rotating at almost the same velocity as during printing after the end of printing, and a secondary cleaning process to press a cleaning fabric previously impregnated with a high viscosity/low volatility cleaning liquid to the cylinder surface with the help of a pressing member, then rotate the blanket cylinder at almost the same velocity as during printing (embodiment example 1) or decelerate the blanket cylinder from the printing velocity to a specified lower velocity level, and rotate the blanket cylinder at the lower velocity for a specified time (embodiment example 2) to clean the cylinder surface, after judging whether the primary cleaning process should be terminated by detection of a degree of web pigmentation.