Radial velocity is one of key measurements in understanding the fundamental properties of stars, stellar clusters and the Galaxy. A plate of stars in the Kepler field were observed in May of 2018 with the medium-resolution spectrographs of LAMOST, aiming to test the performance of this new system which is the upgraded equipment of LAMOST after the first five-year regular survey.We present our analysis on the radial velocity measurements (RVs) derived from these data. The results show that slight and significant systematic errors exist among the RVs obtained from the spectra collected by different spectrographs and exposures, respectively. After correcting the systematic errors with different techniques, the precision of RVs reaches ~1.3, ~1.0, ~0.5 and ~0.3 km/s at S/Nr = 10, 20, 50, and 100, respectively. Comparing with the RVs of the standard stars of the APOGEE survey, our RVs are calibrated with a zero-point shift of ~7 km/s. The results indicate that the LAMOST medium-resolution spectroscopic system may provide RVs in a reasonable accuracy and precision for the selected targets.