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. The LAMOST Medium-Resolution Survey (MRS) DR7 contains 5 million single-exposure stellar spectra at spectral resolution $Rsim7,500$. However, the temporal variation of the RV zero-points (RVZPs) of the MRS survey, which makes the RVs from multiple epochs inconsistent, has not been addressed. In this paper, we measure the RVs of the 3.8 million single-exposure spectra (for 0.6 million stars) with signal-to-noise ratio (SNR) higher than 5 based on cross-correlation function (CCF) method, and propose a robust method to self-consistently determine the RVZPs exposure-by-exposure for each spectrograph with the help of textit{Gaia} DR2 RVs. Such RVZPs are estimated for 3.6 million RVs and can reach a mean precision of $sim 0.38,mathrm{km,s}^{-1}$. 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 analysis. Validating the results with APOGEE DR16 shows that our absolute RVs can reach an overall precision of 0.84/0.80 $mathrm{km,s}^{-1}$ in the blue/red arm at $50<mathrm{SNR}<100$, while 1.26/1.99 $mathrm{km,s}^{-1}$ at $5<mathrm{SNR}<10$. The cumulative distribution function (CDF) of the standard deviations of multiple RVs ($N_mathrm{obs}geq 8$) for 678 standard stars reach 0.45/0.54, 1.07/1.39, and 1.45/1.86 $mathrm{km,s}^{-1}$ in the blue/red arm at 50%, 90%, and 95% levels, respectively. The catalogs of the RVs, RVZPs, and selected candidate RV standard stars are available at url{https://github.com/hypergravity/paperdata}.
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