The invention relates to a flexible connection device of air conditioner pipes. The flexible connection device of the air conditioner pipes comprises a first pipe, a second pipe, a clamping sleeve anda fastening device. A through hole is formed in the clamping sleeve. The first pipe and the second pipe are inserted into the through hole of the clamping sleeve from the two ends of the clamping sleeve. The fastening device is clamped to the clamping sleeve. The two ends of the fastening device are provided with a plurality of elastic bands. One end of each elastic band is fixedly connected withthe fastening device, and the other end of each elastic band is provided with a clasp. Buckling grooves matched with the clasps are formed on the first pipe and the second pipe. The clasps are hookedinto the buckling grooves. The clamping sleeve is made of a flexible material. When the fastening device is clamped, the clamping sleeve clamps and fixes the first pipe and the second pipe, and the clamping sleeve seals the first pipe and the second pipe. The flexible connection device of the air conditioner pipes is reasonable and simple in structure, easy to produce and manufacture and convenient to use. The flexible connection device enables the air conditioner pipes to be flexibly connected, and the flexible connection device has great market application and popularization value.