Inverse kinematics plays a significant role in the robotic motion control. The flexible way to formulate the inverse kinematics can be achieved by using a neural network. The drawback of the neural network-based inverse kinematics is that it has no feedback mechanism to compensate for the remaining error. To improve its performance, further development should be conducted. In the design of the robotic motion control for the NAO robot arms, this paper proposed a new approach that combines the neural network-based inverse kinematics with the Jacobian. This combination yields a closed-loop control system. This control system utilizes the neural network as the feedforward controller and the Jacobian as the feedback controller. In particular, the neural network-based inverse kinematics has a function to estimate a set of required joint angles for the joint actuators, and the Jacobian function is to compensate for the remaining error of the neural network-based inverse kinematics in the estimation of joint angles. By using this proposed approach, we obtained more accurate joint angles for controlling the joint actuators. The comparison result showed that the averaged MSE for the particle swarm optimization (PSO) was 3.47 x 10 -3 rad, 1.19 x 10 -3 rad for the neural network, and 3.72 x 10 -5 rad for the proposed approach. The performance comparison result indicated that our proposed approach has a lower averaged MSE than the other ones. Accordingly, the result of this research confirmed that our proposed approach can provide more accurate joint angles for controlling the joint actuators such that the robot's end-effector can be driven along the desired path in the cartesian space.