During pursuit eye movements, whether the relationships among the visual sensitivity, pursuit velocity, and target velocity are linear or non-linear is an old issue. In this study, we reexamined their relationships with seven speeds by a simple character discrimination task using an infrared eye tracker. Our results found that the pursuit velocity and accuracy were non-linearly related with the target velocity.Besides, the perceptual sensitivity was not linearly related with the pursuit velocity either. A significant difference existed between lower(less than 20 deg/s) and higher speeds(greater than 20 deg/s). In addition, we found there was no position bias of visual sensitivity between ahead of and behind the pursuit target, but there was a significant perceptual dissymmetry between horizontal and vertical directions at lower pursuit speeds. During the pursuit eye movements, whether the relationships among the visual sensitivity, pursuit velocity, and target velocity are linear or non-linear is an old issue. In this study, we reexamined their relationships with seven speeds by a simple character discrimination task using an infrared The results found that the pursuit velocity and accuracy were non-linearly related with the target velocity. Besides, the perceptual sensitivity was not linearly related with the pursuit velocity either. A significant difference existed between lower (less than 20 deg / s ) and higher speeds (greater than 20 deg / s). In addition, we found there was no position bias of visual sensitivity between ahead and behind the pursuit target, but there was a significant perceptual dissymmetry between horizontal and vertical directions at lower pursuit speeds.