The invention belongs to the technical field of coal washing and deashing, relates to a wide-size-fraction flotation system and process and solves problems of complexity, high cost, high energy consumption and environmental hazards in application of an existing wide-size-fraction flotation process. The wide-size-fraction flotation process includes steps: step one, feeding to-be-floated coal slimeinto an agitator, adding water into the agitator, well stirring and mixing, and feeding into a classification cyclone through a first feeding pump to realize preliminary classification; step two, after classification of coal slime is completed in the classification cyclone, feeding overflow in the classification cyclone into a flotation column through a second feeding pump to realize flotation, discharging flotation tailings through an underflow port of the flotation column, collecting flotation concentrate through an overflow port of the flotation column, and feeding into a bubble generator through a fourth feeding pump; step three, feeding underflow in the classification cyclone into a hydraulic flotation machine through a third feeding pump to realize flotation recovery. The process issimple, energy saving and environmental friendliness are realized, and the flotation system is simple in structure and low in cost.