The invention provides a box culvert replacement pipe curtain construction method. The method comprises the steps that 1, a beginning well and a receiving well are constructed at the two sides of a prebuilt channel; 2, a pipe curtain machine jacking device and a pipe curtain machine are installed inside the beginning well, the pipe curtain machine is sequentially jacked through the pipe curtain machine jacking device, and pipe joints are sequentially and continuously jacked to form a pipe curtain of the needed system; 3, a box culvert jacking device is installed; 4, a box culvert is constructed, and the first box culvert is connected with the end face of the pipe curtain; 5, the box culvert jacking device is turned on to sequentially jack the box culvert, the pipe joints are sequentially jacked, the jacked pipe joints are disassembled and excavated; 6, steps 4 and 5 are repeatedly executed till all the pipe joints are disassembled to form a channel; one or two sides, making contact with earth, of the outer sides of the pipe joints and the pipe curtain machine are provided with anti-friction plates, and the pipe curtain machine drives the anti-anti-friction plates to be jacked forwards synchronously.