Previous studies have reported that baseball players have higher than average visual information processing abilities and outstanding motor control. The speed and position of the baseball and the batter are constantly changing, leading skilled players to acquire highly accurate visual information processing and decision-making. This study sought to clarify how movement of the eyes is associated with baseball players’ higher coincident-timing task performance. We recruited 15 right-handed baseball players and 15 age-matched track and field athletes. On a computer-based coincident-timing task, we instructed participants to stop a computer image of a moving target by pressing a button at a designated point. We presented bidirectional moving targets with various velocities, presented in a random order. The targets’ moving angular velocity varied between 100, 83, 71, 63, 56, 50, and 46 deg/s. We conducted 168 repetitions (42 reps × 4 sets) of this coincident-timing task and measured participants’ eye movements during the task using Pupil Centre Corneal Reflection. Mixed-design analysis of variance results revealed participant group effects in favor of baseball players for timing absolute error and low absolute error, as predicted from prior visual processing and decision-making research with baseball players. However, in contrast to prior research, we found significantly shorter smooth-pursuit onset latency in elite baseball players, and there were no significant group differences for saccade onset and offset latencies. This may be explained by the difference in our research paradigm with mobile targets randomly presented at various velocities from the left and right. Our data showed baseball players’ higher than normal simultaneous timing execution for making decisions and movements based on visual information, even under laboratory conditions with randomly moving mobile targets.