A nonlinear spider spring with an initial displacement offset is used to suspend a mass with a coil or permanent magnet and to restore the force spring in order to miniaturize a borehole vertical seismometer with a low natural frequency. We investigate the response properties of the nonlinear spider spring, which remain unknown even though the seismometer adopting nonlinear spider spring is widely used. The relation between the initial offset and the spring constant is clarified for the first time: the spring constant is weakened with increasing initial offset. We confirmed that the flat spider spring has a nonlinear property (as does the spider spring with an offset), although it has previously been considered a linear spring. An analysis of limitations in the use of the seismometer revealed that the nonlinearity can be ignored if the seismometer is used under the condition of small displacement that is recommended by manufacturer.