When we shift our gaze to stare at objects at various distances, not only eye positions but also lens accommodation changes. Usually, visually induced accommodation responses (AccRes) present longer latency than accompanying eye movements, resulting in a brief period of an unfocused retinal image after each gaze shift. Unfocused periods may be extended further when the eyes are under predictive control in response to a temporally periodic visual stimulus. It has been shown that phase lag of the AccRes shortened when the visual target motion was temporally periodic, contributing to reduction of the unfocused periods. However, how rapidly the phase lag shortening is acquired or how long the shortened phase is maintained has been unknown. Presently, we aimed at clarifying the acquisition and maintenance characteristics of the AccRes adaptation. Experiments employing periodic accommodative stimuli revealed that the phase lag is shortened and the gain is temporarily (for 1.3–4 s) increased as early as in the 2nd cycle of the stimulation. Moreover, we show that the adapted AccRes persist for at least 0.25 s in addition to the latency (0.35 s) in the dark after removing periodic visual stimulation. These results add new insights into the temporal characteristics of AccRes adaptation and its maintenance that would play an important role in our daily visual experiences.