The present invention describes a system for drying a web-like paper sheet. The system comprises at least one drying device (12) capable of blowing high temperature dry air, supplied under pressure through one or more inlet conduits (20) on the web-like paper sheet, and of sucking from such a web-like paper sheet the moist air, ejected through one or more outlet conduits (22) connected to a recirculation conduit (26), and a combustion system (20) which comprises at least one hot gas generator (14) of the so-called direct type, provided with a system (16) for supplying fuel and a system (18) for supplying combustion air. The hot gas generator (14) consists of a burner (32), operatively connected to the system (16) for supplying fuel and to the system (18) for supplying combustion air, and of a combustion chamber (38) which is placed in direct fluid communication with the burner ( 32) by interposing a connection conduit (40). Outside the combustion chamber (38) at least one cooling channel (34) is provided, which encloses such a combustion chamber (38). The cooling channel (34) is placed downstream of the burner (32) and is operatively connected to the recirculation conduit (26), so that the hot gas generator (14) is capable of generating an air and burnt gases mixture which forms the dry air, as well as receiving, through such a recirculation conduit (26), at least part of the moist air so that it can be heated and reutilised by the drying device (12).