This paper presents the design and analysis of a three-fingered deployable metamorphic robotic grasper for manipulating large-scale unknown objects. This grasper is composed of three fingers and a single-mobility umbrella-shaped palmar mechanism. First, the mechanism-design of the grasper is introduced and the metamorphic-motion process is analyzed, followed by the structural optimization, the finger with three modules can be deployed from 111.5 mm to 304 mm, and the good deploy/fold ratio can reach 2.73. This equips the grasper with a compact folded configuration and a large deployed configuration. Second, kinematic models of the deployment motion and grasping motion are independently established, and kinematic analysis is conducted. To further illustrate kinematic performance, kinematic simulation for the grasper is then performed. Third, the condition of the stable grasp is analyzed; trajectory planning of the grasper based on an S-shaped acceleration and deceleration function algorithm is then carried out. Fourth, a control system is designed and a physical prototype is fabricated. Grasping experiments are then conducted to prove the ability of the grasper to grasp objects of various sizes and shapes.