Radial velocity (RV) is among the most fundamental physical quantities obtainable from stellar spectra and is rather important in the analysis of time-domain phenomena. LAMOST Medium-Resolution Survey (MRS) DR7 contains five million single-exposure stellar spectra with spectral resolution R~7500. However, the temporal variation of the RV zero-points (RVZPs) of the MRS, which makes the RVs from multiple epochs inconsistent, has not been addressed. In this paper, we measure the RVs of 3.8 million single-exposure spectra (for 0.6 million stars) with signal-to-noise ratios (S/N) higher than 5 based on the cross-correlation function method, and propose a robust method to self-consistently determine the RVZPs exposure by exposure for each spectrograph with the help of Gaia DR2 RVs. Such RVZPs are estimated for 3.6 million RVs and can reach a mean precision of ~0.38km/s. The result of the temporal variation of RVZPs indicates that our algorithm is efficient and necessary before we use the absolute RVs to perform time-domain analyses. Validating the results with APOGEE DR16 shows that our absolute RVs can reach an overall precision of 0.84/0.80km/s in the blue/red arm at 50<S/N<100 and of 1.26/1.99km/s at 5<S/N<10. The cumulative distribution function of the standard deviations of multiple RVs (N_obs_>=8) for 678 standard stars reaches 0.45/0.54, 1.07/1.39, and 1.45/1.86km/s in the blue/red arm at the 50%, 90%, and 95% levels, respectively.