To provide a tension controller and an offset rotary press that includes no dampening water, a dryer or a cleaning device, keeps constant print quality during normal printing, and reduces waste paper when tension disturbance occurs.

The tension controller includes: a means provided on the upstream of the most upstream print unit and the downstream of the most downstream print unit among one or more printing units for performing print on a print web, for measuring tension; a means for calculating the control amount of a conveyance speed of the print web so that the tension becomes closer to a predetermined value on the basis of a measured result; and a means for controlling the conveyance speed on the basis of the control amount of the conveyance speed. The means for controlling the conveyance speed is provided on the upstream of the means for measuring the tension on the upstream of the most upstream print unit. The means for controlling the conveyance speed is provided on the downstream of the means for measuring the tension on the downstream of the most downstream print unit.