This study proposes a teleoperation system based on a six-degree-of-freedom robot arm, aiming to design a non-wearable and intuitive control method. The system uses a Kinect V1 camera and a UR3 robot arm, with the Microsoft skeleton recognition library as the basic method for human pose recognition. By mapping the human arm to the robot arm joints, the robot arm can track the motion of the human arm in real-time. Meanwhile, the nonlinear model predictive control (NMPC) algorithm is used to optimize the robot arm motion control, and fuzzy rules are set to achieve adaptive adjustment of NMPC parameters. The experimental results show that under the optimization of NMPC, the robot arm has significantly reduced average displacement and rotation errors in both the x and z translation directions and the three rotational directions, as well as average error in joint angle changes. The test results also demonstrate that the overall motion tracking performance of the robot arm is good, verifying the accuracy of the proposed mapping rules and kinematic model, as well as the effectiveness of the fuzzy NMPC controller.