A cosmetic container having a storage container for housing a liquid- or gel-form basic cosmetic and a granulated cosmetic having a different function from the basic cosmetic, an airless pump on top of the storage container for discharging the mixed cosmetics from the storage container, and pulverization apparatus including a pulverizing member, a first pulverizing mesh and a second, finely pulverizing mesh positioned in a plurality of stages in a discharge pathway within the airless pump to cause the granulated cosmetic in the mixed cosmetics to be finely pulverized in a plurality of stages, with multistage smashing and fine pulverization of the granulated cosmetic in the pump such that discharge of the cosmetic is thereby performed smoothly when the cosmetic is used.