There are provided a liquid jetting apparatus in which the deterioration of production efficiency is suppressed in a case in which the floating of a medium occurs, and a method of coping with the floating of a medium. A medium is fed; liquid is jetted to the medium, which is transported by a medium transport unit including a medium support surface on which the medium is supported and transporting the fed medium in a medium transport direction, by a liquid jet head; drying processing is performed on the medium, to which the liquid jetted from the liquid jet head adheres, at a position on the downstream side of the liquid jet head in the medium transport direction; and in a case in which the floating of the medium is detected at a position on the upstream side of the liquid jet head in the medium transport direction, the medium continues to be fed, the liquid jet head is moved to a retreat position from a liquid jet position, and the intensity of drying processing is suppressed in comparison with that in a liquid-drying processing-performing state in which drying processing is performed on the medium.