The invention discloses a clamping apparatus of a variable-pitch flexible robot. The clamping apparatus comprises a clamping apparatus framework (1). The bottom of a top plate of the clamping apparatus framework (1) is provided with two cylinders (2) opposite in driving direction. At least two suckers (3) are arranged in the clamping apparatus framework (1). The bottoms of the suckers (3) are provided with sucker flexible joints (4). Connecting blocks (5) are fixedly installed on the suckers (3). Meanwhile, cylinder push blocks (6) are fixedly arranged on the connecting blocks (5) on the sides of the two ends of the clamping apparatus framework (1) in the length direction of the clamping apparatus framework (1) and are connected with piston rods of the cylinders (2) through corresponding cylinder connecting rods (7). When the piston rods of the two cylinders (2) stretch out, the corresponding suckers (3) are far away from each other, and otherwise, the corresponding suckers (3) get close to each other. The clamping apparatus can adjust the distance between the suckers in real time, the binning requirement of ice cream of different kinds and at different intervals is met, and the application range is wide.