Focusing 8 keV x rays to a spot size of 150 and 90 nm full width at half maximum has been demonstrated at the first- and third-order foci, respectively, of a phase zone plate at the Advanced Photon Source 2-ID-D x-ray microprobe experiment station [Yun et al., Rev. Sci. Instrum. 70, 2238 (1999)]. In order to perform an x-ray microprobe experiment with such a high spatial resolution, vibration control of the x-ray microprobe supporting system becomes a critical issue. Recently, we have designed and constructed a vibration-damping structure for the APS 2-ID-D x-ray microprobe experiment station. In this article the vibration-damping structure design as well as the vibration test results for the x-ray microprobe supporting system are presented. This is an essential improvement toward future operation of the microprobe at sub-100-nm spatial resolution.