Subjects were given reflexive- and voluntary-saccade tasks using five different gap intervals (0–500 ms) between the fixation point offset and the target onset and an overlap paradigm (i.e., the fixation point remained on during the target presentation). In the first experiment, targets were monocularly presented, and the latencies of reflexive saccades to a peripheral target were compared between the left and right visual fields in which targets were presented. The data averaged over subjects did not show a significant difference of saccade latencies between the two visual fields. However, individual subjects showed strong left/right asymmetries of saccade latencies: six out of the 12 subjects that participated made a saccade more rapidly to the right than to the left, and two other subjects showed the reverse result. In these cases, the left/right asymmetry was observed on both gap and overlap trials. The saccade latencies were not affected by the hemiretina to which a target was projected. The second experiment was conducted to identify conditions under which the left/right asymmetry can be reproduced. For this purpose, five subjects were given both reflexive-saccade and voluntary-saccade tasks. In the latter task, a cue stimulus for generating saccades was given at the central fixation point. Regardless of whether saccades were made reflexively or voluntarily, and whether the targets were viewed monocularly or binocularly, each subject showed the same pattern of left/right asymmetries of saccade latencies. The results were interpreted as showing that a visuo-spatial attentional bias specific to individual subjects is involved in generating idiosyncratic left/right asymmetries of saccade latencies.