The purpose of this paper is to quickly and stably achieve grasping objects with a 3D robot arm controlled by electrooculography (EOG) signals. A EOG signal is a biological signal generated when the eyeballs move, leading to gaze estimation. In conventional research, gaze estimation has been used to control a 3D robot arm for welfare purposes. However, it is known that the EOG signal loses some of the eye movement information when it travels through the skin, resulting in errors in EOG gaze estimation. Thus, EOG gaze estimation is difficult to point out the object accurately, and the object may not be appropriately grasped. Therefore, developing a methodology to compensate, for the lost information and increase spatial accuracy is important. This paper aims to realize highly accurate object grasping with a robot arm by combining EMG gaze estimation and the object recognition of camera image processing. The system consists of a robot arm, top and side cameras, a display showing the camera images, and an EOG measurement analyzer. The user manipulates the robot arm through the camera images, which can be switched, and the EOG gaze estimation can specify the object. In the beginning, the user gazes at the screen’s center position and then moves their eyes to gaze at the object to be grasped. After that, the proposed system recognizes the object in the camera image via image processing and grasps it using the object centroid. The object selection is based on the object centroid closest to the estimated gaze position within a certain distance (threshold), thus enabling highly accurate object grasping. The observed size of the object on the screen can differ depending on the camera installation and the screen display state. Therefore, it is crucial to set the distance threshold from the object centroid for object selection. The first experiment is conducted to clarify the distance error of the EOG gaze estimation in the proposed system configuration. As a result, it is confirmed that the range of the distance error is 1.8–3.0 cm. The second experiment is conducted to evaluate the performance of the object grasping by setting two thresholds from the first experimental results: the medium distance error value of 2 cm and the maximum distance error value of 3 cm. As a result, it is found that the grasping speed of the 3 cm threshold is 27% faster than that of the 2 cm threshold due to more stable object selection.