Movements of the visual scene evoke short-latency ocular-following-responses (OFR). Many studies suggest that a neural pathway containing the cerebellar-ventral-paraflocculus (VPFL) mediates OFR. The relationship between eye movement and simple-spike firing in the VPFL during OFR has been studied in detail using an inverse dynamics approach. The relationship between eye movement and cell firing in the extraoculomotor nucleus (MN) has already been reported. However, no studies have examined the information transformation that occurs between the VPFL and the MN during OFR. In this paper, using an inverse dynamics approach, we derive a transfer function that represents the characteristics of the structure connecting the VPFL and the MN during upward OFR. This structure appears to contain a kind of neural integrator, which constructs eye-velocity-and-position information from eye-acceleration-and-velocity information. We propose a diagram for the neural integration commonly at work during all types of upward eye movement. This is a closed-loop circuit containing a low-pass filter. The low-pass filter can construct eye-velocity-and-position information from an eye-acceleration-velocity-position command similar to the final motor command used commonly for all upward eye movements. Anatomical and electrophysiological data suggest that the vestibular nuclei-interstitial nucleus of Cajal-vestibular nuclei loop might perform such neural integration.