The invention discloses a prestress fiber reinforced polymer cable anchoring device adopting a grooved clamping piece, which includes an anchoring block, a polymer cable anchor clamping piece arranged in each opening of the anchoring block, and fiber reinforced polymer cables arranged in each polymer anchor clamping piece, wherein each polymer cable anchor clamping piece adopts an integral structure, and both ends of each polymer cable anchor clamping piece are longer than the opening of the anchoring block; n vertical grooves are formed in the main body of each polymer cable anchor clamping piece. The anchoring device can be used for anchoring the FRP (fiber reinforced polymer) cables, a certain angle is kept between the front part on the outer surface of the clamping piece to the bottom, so as to be matched with the inner surface of the anchoring block, the inner surface of the anchoring block subjected to drawing force exerts extrusion force on the clamping piece, so that the clamping pieces are extruded and deformed at the grooves, can clamp the polymer cables as the inner diameter is reduced, the clamping pieces are longer than the anchoring block, the front part and the bottom of the clamping pieces are exposed and longer than the anchoring block for a certain length, as a result, forward and backward anchor retreat can be realized.