We present new radial velocity measurements for 82 stars , members of the Galactic globular cluster NGC 6388 , obtained from ESO-VLT KMOS spectra acquired during the instrument Science Verification . The accuracy of the wavelength calibration is discussed and a number of tests of the KMOS response are presented . The cluster systemic velocity obtained ( 81.3 \pm 1.5 km s ^ { -1 } ) is in very good agreement with previous determinations . While a hint of ordered rotation is found between 9 \arcsec and 20 \arcsec from the cluster centre , where the distribution of radial velocities is clearly bimodal , more data are needed before drawing any firm conclusions . The acquired sample of radial velocities has been also used to determine the cluster velocity dispersion profile between \sim 9 \arcsec and 70 \arcsec , supplementing previous measurements at r < 2 \arcsec and r > 60 \arcsec obtained with ESO-SINFONI and ESO-FLAMES spectroscopy , respectively . The new portion of the velocity dispersion profile nicely matches the previous ones , better defining the knee of the distribution . The present work clearly shows the effectiveness of a deployable Integral Field Unit in measuring the radial velocities of individual stars for determining the velocity dispersion profile of Galactic globular clusters . It represents the pilot project for an ongoing large program with KMOS and FLAMES at the ESO-VLT , aimed at determining the next generation of velocity dispersion and rotation profiles for a representative sample of globular clusters .