An integrated apparatus that contains both the gravity settling mechanism and the dissolved-air floatation (DAF) mechanism in a compensating manner is provided. The said apparatus comprises a gravity settling chamber (34), a DAF chamber (42), a chamber connection channel (22), an air-dissolving device (38), a means for collecting treated water (24), and a water level control device (16). During treatment, heavy solid particles in water or wastewater can be quickly removed by gravity settling, while the remaining light solid particles and/or oil can be quickly removed by DAF. Thus, the apparatus of this invention is more effective and efficient compared with conventional clarifiers that employ only one clarification mechanism. Therefore, the apparatus of this invention is more compact and can achieve better effluent quality.