The invention discloses a flexible casing treatment centrifugal compressor. The flexible casing treatment centrifugal compressor comprises a volute and an impeller, air outlet channels are formed in the two side ends in the volute, an air inlet is formed in the position, on an air inlet channel, of the front side surface of the volute, air outlets are formed in the positions, on the air outlet channels, of the two side ends in the volute, an impeller mounting cavity communicates with the air inlet channel and the air outlet channels, casing grooves are formed in the two side walls of the air inlet channel, partition boards are transversely and fixedly arranged in the casing grooves, flexible baffles are arranged on the side surfaces of the partition boards, and gaps are formed between theouter side ends of the flexible baffles and the bottom surfaces of the casing grooves. The compressor carries out operation on the basis of not changing an original centrifugal compressor volute casing treatment mechanism, the compressor is simple and convenient, flowing losses are avoided to a certain degree while the stable work range of the centrifugal compressor is further widened, and the reduction of the efficiency of the centrifugal compressor is effectively prevented.