The invention discloses a tensioning and anchoring device for prestressed fiber cloth reinforced beams and a construction method of the device. The device comprises fixed supports, a fixed end anchorage device, a tensioning end anchorage device, clamping pieces, short anchoring screws, long anchoring screws, chemical bolts, fiber cloth, a prestress application frame and a jack, wherein the fixed supports, the fixed end anchorage device and the tensioning end anchorage device are cuboid; the fixed supports are fixed with a to-be-reinforced beam through the chemical bolts; the fixed end anchorage device and the tensioning end anchorage device are connected with the fixed supports through the short anchoring screws and the long anchoring screws respectively; a rectangular through seam allowing the fiber cloth to pass is formed in the fixed end anchorage device; wedge-shaped holes allowing insertion of the clamping pieces are formed in the tensioning end anchorage device, and the clampingpieces are wedged into the wedge-shaped holes, so that clamping of the fiber cloth is realized. The construction method comprises steps as follows: firstly, the anchorage devices are mounted, then thefixed supports are assembled and the anchorage devices are fixed, finally, the prestress application frame and the jack are mounted, and tensioning and anchoring are implemented. The device is reasonable and simple in structure and convenient to operate and can be reused, and the applied prestress is large.