Human activities are often performed together between two or more persons, as if they are a complex dance. Threading through a crowd is a striking example of such coordinated actions. Behavioral coordination should help to reduce head-on collisions, smooth a pedestrian's pathway through a crowd, and promote a self-organization process. Although mutual anticipation between pedestrians would be a candidate for underlying mechanisms of behavioral coordination, it remains largely unexplored, especially in terms of visual information. Here, we investigated the effects of mutual anticipation between a pair of pedestrians performing simple avoidance tasks using a combination of motion- and eye-tracking systems. We found that pedestrians in a baseline condition spontaneously coordinated their walking speed and angle until passing each other. Visually distracting one of the pedestrians decreased the level of behavioral coordination, indicating that spontaneous coordination emerges through mutual anticipation. Importantly, blocking the pedestrians' gaze information alone did not alter their walking, clearly ruling out the assumption that mutual gaze impacts pedestrian anticipation behavior. Moreover, eye-movement analysis demonstrated that the direction of a pedestrian's gaze changed depending on the uncertainty of the oncoming pedestrian's motion and that pedestrians tend to look ahead toward the ultimate passing direction before they actually walked in that direction. We propose that body motion cues may be sufficient and available for implicit negotiation on potential future motions. Our findings should be useful in various fields, including research on improvisational motions, pedestrian transportation, and robotic navigation.