Due to the low motion efficiency and maneuver-ability of underwater robots with six degrees of freedom, it is challenging for them to respond quickly to the attitude requirements during underwater autonomous manipulation. This paper presents a novel autonomous underwater robot with fully vectored propulsion and a model predictive control method to achieve more agile and efficient movements autonomously. In detail, we first design a robot with eight vector-distributed thruster layouts for fully vectored propulsion and construct the software architecture based on the robot operating system (ROS). Then, we establish the hydrodynamic model by adopting the Fossen approach and construct a 13-dimensional system state-space equation, which is discretized using the explicit fourth-order Runge-Kutta method. To achieve autonomous manipulation, model predictive control is employed along with physical constraints of the custom-built robot to enable real-time prediction and optimization of the robot’s states for control purposes. Finally, numerical simulations and experiments of the Point-to-Point Motion are conducted to test the robot’s performance. Experimental results reveal that the average error of each direction is 0.0027 m, 0.0031 m, and 0.0368 m in the x-axis, y-axis, and z-axis, respectively, and 0.8502°, 2.1941°, 0.2408° corresponding to three attitude angles, which verify the performance of employing MPC to control an autonomous underwater robot with fully vectored propulsion.