The LAMOST Medium-Resolution Spectroscopic Survey (LAMOST-MRS) provides an unprecedented opportunity for detecting multi-line spectroscopic systems. Based on the method of Cross-Correlation Function (CCF) and successive derivatives, we search for spectroscopic binaries and triples and derive their radial velocities (RVs) from the LAMOST-MRS spectra. A Monte-Carlo simulation is adopted to estimate the RV uncertainties. After examining over 1.3 million LAMOST DR7 MRS blue arm spectra, we obtain 3,133 spectroscopic binary (SB) and 132 spectroscopic triple (ST) candidates, which account for 1.2% of the LAMOST-MRS stars. Over 95% of the candidates are newly discovered. It is found that all of the ST candidates are on the main sequence, while around 10% of the SB candidates may have one or two components on the red giant branch.