  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 $R\sim7\,500$.
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}.
