A mathematical model that accurately reproduces eye movements from visual stimuli and incorporates intermediate neural signals is useful for quantitative analysis of the neural mechanisms involved in transforming visual stimuli to eye movements. Here we describe a mathematical model consisting of two systems: a non-linear system that relates retinal slip to simple spike firing frequency of Purkinje cells in the ventral paraflocculus (VPFL) and a linear system that relates VPFL simple spike firing frequency to eye movement. This model accurately reproduced the firing frequency of Purkinje cells and ocular following responses from visual stimulation paradigms used in physiological experiments.