This paper proposes a novel operation for controlling a mobile robot using a head-mounted device. Conventionally, robots are operated using computers or a joystick, which creates limitations in usability and flexibility because control equipment has to be carried by hand. This lack of flexibility may prevent workers from multitasking or carrying objects while operating the robot. To address this limitation, we propose a hands-free method to operate the mobile robot with a human gaze in an Augmented Reality (AR) environment. The proposed work is demonstrated using the HoloLens 2 to control the mobile robot, Robotnik Summit-XL, through the eye-gaze in AR. Stable speed control and navigation of the mobile robot were achieved through admittance control which was calculated using the gaze position. The experiment was conducted to compare the usability between the joystick and the proposed operation, and the results were validated through surveys (i.e., SUS, SEQ). The survey results from the participants after the experiments showed that the wearer of the HoloLens accurately operated the mobile robot in a collaborative manner. The results for both the joystick and the HoloLens were marked as easy to use with above-average usability. This suggests that the HoloLens can be used as a replacement for the joystick to allow hands-free robot operation and has the potential to increase the efficiency of human-robot collaboration in situations when hands-free controls are needed.