The underwater flexible robot is a field of continuous exploration and innovation. An underwater flexible manipulator with the functions of bending and grasping is presented in this paper, which is driven by the water hydraulic. The flexible manipulator is consisted mainly of three sets of transverse and three sets of longitudinal Mckibben artificial muscles (MAM) equidistantly arranged. The motions of the manipulator were driven by accurately controlling the length of each MAM that was changed by controlling the internal pressure, which was provided by the hydraulic power subsystem. The flexible manipulator was controlled remotely by the control subsystem. The inverse kinematics of the flexible manipulator was studied based on the neural network in this paper. The feasibility of the neural network inverse kinematics was proved by the data analysis. The three-dimensional virtual model of the flexible manipulator was projected into the captured real scene by the augmented reality (AR) technology to judge the bending degree of the manipulator operation, which could be seen in the experiment image.