The underwater swimming manipulator (USM) is a new type of underwater robot composed of an underwater snake robot and several thrusters. The USM system has the characteristics of high nonlinear and uncertainty, and its dynamic model is difficult to establish accurately. Therefore, it is challenging to achieve high precision stabilization control of USM. To solve this problem, this paper designs a dynamic control framework based on feedback linearization and adaptive radial basis function neural network (RBFNN) for USM stabilization control. Firstly, the structure of the USM platform is introduced, the dynamic model of the USM is established based on the Lagrange equation, and the model of the vector thrust system is derived. Then, a dynamic controller based on feedback linearization and RBFNN is designed, and the weight of RBFNN is updated adaptively by backstepping method. Among them, the weight adaptive updating RBFNN is used to estimate the unmodeled part of the system, parameter errors and external disturbances, so as to compensate the dynamics controller. In addition, in order to convert the generalized forces and torques provided by the dynamic controller into the control inputs of each actuator, a thrust distribution strategy is given. Finally, lake experiments are carried out to stabilize the I-shape and C-shape of USM respectively. Compared with traditional methods, the steady-state errors of the proposed control scheme under both configurations are less than 0.08 m and 10°, which verifies the effectiveness of the proposed 6-DOF USM stabilization controller.