Recently, a linear ball guideway is often used for precision and ultra-precision positioning. Rolling elements such as linear ball guideways have static characteristic called Nonlinear Spring Behavior (NSB) in minute displacement. And these rolling elements have frequency response characteristic of dynamic characteristic when positioning. As this characteristic has resonant point and the guideway vibrates, it is very difficult problem to achieve the precision and ultra-precision positioning. Measuring dynamic characteristic is not easy and takes times. Then, the precision positioning device of an axis using a Voice Coil Motor (VCM) is composed to measure the NSB and the frequency response. Resonant frequency presumed from the spring constant of the obtained nonlinear spring behavior and damping ratio presumed as a function of displacement using least square method correspond to ones of the frequency response respectively. Therefore, this paper shows that it is possible to estimate the frequency response characteristic only using result of the nonlinear spring behavior.