The invention provides a self-balancing fuel assembly grabbing mechanism which comprises a roller rail, an upper balancing roller, a transmission shaft, a lower bracket, an upper bracket, a balancing cam and fuel assembly claws. The upper balancing roller is limited in the roller rail to translate. The lower part of the roller rail is fixedly connected with the upper end of the transmission shaft. The lower part of the transmission shaft is inserted in the middle of the lower bracket. The upper part of the lower bracket is located in the upper bracket. The upper part of the upper bracket is mounted on a support through a radial bearing. The upper bracket can rotate in the axial direction. The lower part of the upper bracket is connected with the lower bracket through the balancing cam. The fuel assembly claws are arranged on the lower bracket. The interior of each fuel assembly claw adopts a slotted structure. The lower end of the transmission shaft moves up and down in a groove. The self-balancing fuel assembly grabbing mechanism provided by the invention can be used for maintaining balancing of the fuel assembly claws to realize stable and vertical lifting and releasing of a fuel assembly.