In the position control of the mechanical arm of an iron roughneck (MAIR), a controller with high responsiveness, high accuracy, and high anti-interference capability is necessary. An MAIR consists of two proportional-valve-controlled single-extension (PVCSE) hydraulic cylinders, and a traditional proportional−integral−derivative (PID) controller cannot easily achieve the accuracy and robustness requirements of the hydraulic cylinders. In this paper, a three-dimensional fuzzy active disturbance rejection controller (TF-ADRC) is proposed for an MAIR, which adds a three-dimensional fuzzy module to a classical active disturbance rejection controller (ADRC) to adjust the controller output according to the tracking of differential deviation, deviation change rate, and deviation change acceleration rate. Firstly, the trajectory planning of the MAIR was carried out using the quintic polynomial interpolation method to improve the smoothness of the target trajectory. Then, the reliability of the established model was verified by experiments. Finally, the comprehensive performance of a PID controller, fuzzy PID controller, ADRC, and TF-ADRC were compared based on the AMESim-Simulink model. The system with the TF-ADRC exhibits higher position control accuracy and better anti-interference capability than the system with a PID or Fuzzy PID controller, and accuracy is higher compared with the common ADRC.