In this paper, we measured the tracking response time of horizontal eye movement to the target moving according to the square waveform to investigate the predictive characteristics of the human oculomotor system. And in the experiment we used the square waves with an amplitude of 5 degree and frequencies o.1, 0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 Hz. Random occurrences of the human eye movement reponse time were analyzed using a finite Markov chain process and we found the results as follows. From both the experimental and theoretical results, we found the trend showing that Predictive characteristics moved from the transient state to the steady state.