Rock bolting is a commonly used method for stabilizing the surrounding rock in coal-mine roadways. It involves installing rock bolts after drilling, which penetrate unstable rock layers, binding loose rocks together, enhancing the stability of the surrounding rock, and controlling its deformation. Although recent progress in drilling and anchoring equipment has significantly enhanced the efficiency of roof support in coal mines and improved safety measures, how to deal with drilling rigs’ misalignment with the through-hole center remains a big issue, which may potentially compromise the quality of drilling and consequently affect the effectiveness of bolt support or even result in failure. To address this challenge, this article presents a robotic teleoperation system alongside a hybrid visual servo control strategy. Addressing the demand for high precision and efficiency in aligning the drilling rigs with the center of the drilling hole, a hybrid control strategy is introduced combining position-based and image-based visual servo control. The former facilitates an effective approach to the target area, while the latter ensures high-precision alignment with the center of the drilling hole. The robot teleoperation system employs the binocular vision measurement system to accurately determine the position and orientation of the drilling-hole center, which serves as the designated target position for the drilling rig. Leveraging the displacement and angle sensor information installed on each joint of the manipulator, the system utilizes the kinematic model of the manipulator to compute the spatial position of the end-effector. It dynamically adjusts the spatial pose of the end-effector in real time, aligning it with the target position relative to its current location. Additionally, it utilizes monocular vision information to fine-tune the movement speed and direction of the end-effector, ensuring rapid and precise alignment with the target drilling-hole center. Experimental results demonstrate that this method can control the maximum alignment error within 7 mm, significantly enhancing the alignment accuracy compared to manual control. Compared with the manual control method, the average error of this method is reduced by 41.2%, and the average duration is reduced by 4.3 s. This study paves a new path for high-precision drilling and anchoring of tunnel roofs, thereby improving the quality and efficiency of roof support while mitigating the challenges associated with significant errors and compromised safety during manual control processes.