A small oxygen enriching apparatus which can supply oxygen-enriched gas at high flow rate without imparting unnatural sensation to a user, as well as a controller and recording medium therefore. In step 100, a judgment is made as to whether a flow rate set by use of a flow-rate setting unit 47 is equal to or less than a continuous base flow rate (2 liters/min). When the set flow rate is a low flow rate of not greater than 2 liters/min, breath-synchronized operation is not performed (continuous supply is to be performed), and therefore, in step 110, oxygen-enriched gas is supplied continuously at the set flow rate. When the set flow rate is a high flow rate of greater than 2 liters/min, breath-synchronized operation is to be performed (supply during the inhalation period only of each breathing cycle), and therefore, in step 120, oxygen-enriched gas is continuously supplied at the continuous base flow rate. In step 140, in order to perform breath-synchronized operation, control for opening and closing an electromagnetic valve 45 is performed. That is, oxygen-enriched gas is supplied during the inhalation period only of each breathing cycle, and supply of oxygen-enriched gas is stopped during the exhalation period.