To enable calcium ions being eluted from ink or printing paper to be effectively removed.

In this damping water circulating method for offset printing, damping water is circulated between a storage tank 11 for storing the damping water for which an etching liquid is diluted with water, and a water tank of a printing unit section. In the method, a calcium ion concentration is measured in each of damping water circulating paths 12 and 13 and a water replenishing path 14 before the etching water is mixed. The necessary amount of a chelating agent for concealing calcium being eluted from the ink or the printing paper is calculated from a difference in those measured values. By making the calcium ion into a complex by adding the chelating agent of the calculated amount, the formation of sludge by the reaction with phosphor can be prevented from occurring, and the generation of a roller strip resulting from the sludge is eliminated.