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Searching for compact objects (black holes, neutron stars, or white dwarfs) in the Milky Way is essential for understanding the stellar evolution history, the physics of compact objects, and the structure of our Galaxy. Compact objects in binaries with a luminous stellar companion are perfect targets for optical observations. Candidate compact objects can be achieved by monitoring the radial velocities of the companion star. However, most of the spectroscopic telescopes usually obtain stellar spectra at a relatively low efficiency, which makes a sky survey for millions of stars practically impossible. The efficiency of a large-scale spectroscopic survey, the Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST), presents a specific opportunity to search for compact object candidates, i.e., simply from the spectroscopic observations. Late-type K/M stars are the most abundant populations in our Galaxy. Owing to the relatively large Keplerian velocities in the close binaries with a K/M-dwarf companion, a hidden compact object could be discovered and followed-up more easily. In this study, compact object candidates with K/M-dwarf companions are investigated with the LAMOST low-resolution stellar spectra. Based on the LAMOST Data Release 5, we obtained a sample of $56$ binaries, each containing a K/M-dwarf with a large radial velocity variation $ΔV_{\rm R} > 150~{\rm km~s}^{-1}$. Complemented with the photometric information from the Transiting Exoplanet Survey Satellite, we derived a sample of $35$ compact object candidates, among which, the orbital periods of $16$ sources were revealed by the light curves. Considering two sources as examples, we confirmed that a compact object existed in the two systems by fitting the radial velocity curve. This study demonstrates the principle and the power of searching for compact objects through LAMOST.