The invention relates to the field of automatic control and discloses an oxygen-supply control device and method of an oxygen-enriched combustion system. The control device comprises a measuring module and a processing module. During a switchover of the oxygen-enriched combustion system from an air combustion condition to an oxygen-enriched combustion condition, the measuring module is used for measuring oxygen flow rate supplied to a primary air re-circulating gas duct, oxygen flow rate supplied to a secondary air re-circulating gas duct, value of oxygen concentration in primary air mixed flue gas and value of oxygen concentration in secondary air mixed flue gas. The processing system is used for converting the oxygen flow rate supplied to the primary air re-circulating gas duct into first value of oxygen concentration and regulating an oxygen-injection regulation valve of the primary air re-circulating gas duct based on the first value of oxygen concentration and the value of oxygen concentration of the primary air mixed flue gas and also used for converting the oxygen flow rate supplied to the secondary air re-circulating gas duct into the second value of oxygen concentration and regulating an oxygen-injection regulation valve of the secondary air re-circulating gas duct based on the second value of oxygen concentration and the value of oxygen concentration of the secondary air mixed flue gas. The oxygen-supply control device and method of the oxygen-enriched combustion system are capable of rapidly and uniformly mixing high-concentration oxygen or pure oxygen and recycled flue gas according to the proportion required by boiler combustion.