A control rod/fuel support handling apparatus that is used in the case where a control rod and a fuel support are held, removed and lifted in a reactor and then are transported into the reactor in a periodical inspection of a BWR and in the case where the control rod and the fuel support are attached and mounted again into the reactor, the control rod/fuel support handling apparatus including: a fuel support gripper that holds the fuel support with a support gripping member; a control rod gripper that includes a vertically movable and rotatable elevating/rotating unit, holds the control rod with a control rod gripping member, disconnects and connects the control rod and a control rod drive mechanism, and allows removal and attachment of the control rod; and a control panel that controls automatically controls the control rod gripper in response to the instructions from an operation pendant.