A beta-ray detecting nuclear quadrupole resonance system has been developed at NSCL/MSU to measure ground-state electric quadrupole moments of short-lived nuclei produced as fast rare isotope beams. This system enables quick and sequential application of multiple transition frequencies over a wide range. Fast switching between variable capacitors in resonance circuits ensures sufficient power delivery to the coil in the beta-ray detecting nuclear magnetic resonance technique. The fast switching technique enhances detection efficiency of resonance signals and is especially useful when the polarization and/or production rate of the nucleus of interest are small and when the nuclear spin is large.