The subjective feeling of being the author of one's actions and the subsequent consequences is referred to as a sense of agency. Such a feeling is crucial for usability in human-computer interactions, where eye movement has been adopted, yet this area has been scarcely investigated. We examined how the temporal action-feedback discrepancy affects the sense of agency concerning eye movement. Participants conducted a visual search for an array of nine Chinese characters within a temporally-delayed gaze-contingent display, blurring the peripheral view. The relative delay between each eye movement and the subsequent window movement varied from 0 to 4,000 ms. In the control condition, the window played a recorded gaze behavior. The mean authorship rating and the proportion of "self" responses in the categorical authorship report ("self," "delayed self," and "other") gradually decreased as the temporal discrepancy increased, with "other" being rarely reported, except in the control condition. These results generally mirror those of prior studies on hand actions, suggesting that sense of agency extends beyond the effector body parts to other modalities, and two different types of sense of agency that have different temporal characteristics are simultaneously operating. The mode of fixation duration shifted as the delay increased under 200-ms delays and was divided into two modes at 200-500 ms delays. The frequency of 0-1.5° saccades exhibited an increasing trend as the delay increased. These results demonstrate the influence of perceived action-effect discrepancy on action refinement and task strategy.