The radial velocity (RV) is a basic physical quantity that can be determined through the Doppler shift of the spectrum of a star. The precision of the RV measurement depends on the resolution of the spectrum we used and the accuracy of wavelength calibration. In this work, radial velocities of the Large Sky Area Multi-Object Fibre Spectroscopic Telescope-II (LAMOST-II) medium-resolution (R~7500) spectra are measured for 1,594,956 spectra (each spectrum has two wavebands) through matching with templates. A set of RV standard stars are used to recalibrate the zero point of the measurement, and some reference sets with RVs derived from medium-/high-resolution observations are used to evaluate the accuracy of the measurement. By comparing with reference sets, the accuracy of our measurement can get 0.0277km/s with respect to radial velocities of standard stars. The intrinsic precision is estimated with the multiple observations of single stars, which can be achieved to 1.36km/s, 1.08km/s, and 0.91km/s for the spectra at signal-to-noise levels of 10, 20, and 50, respectively.