PURPOSE: To efficiently dry in drying by pressing a paper web to a heat roller by bringing steps in 3 steps of a pre-heating and pressing step, a water vaporization-accelerating step and a nip-pressing step.

CONSTITUTION: In drying a paper web by pressing to a hot roller heated at ≥100°C, the drying is carried out in 3 steps, i.e., a pre-heating and pressing step of applying a relatively low compression pressure for a relatively long hours, a step of decreasing the compression pressure and accelerating vaporization of water in the paper web and a nip-pressing step of applying a high compression pressure. For example, a paper web W is passed through along a pressing felt 12 between a heating roller (cylinder) 10 having ≥100°C surface temperature and an endless sliding belt 25. On the back side of the endless slide belt 25, a press shoe device 30 and a press roller 20 are installed in order and the pre-heating and pressing step and the nip-pressing step are carried out by those devices and the water vaporization-accelerating step is carried out between those devices.