We report the discovery of one possible neutron star binary (P_orb_=0.8666d) by using LAMOST low-resolution spectroscopic data. The visible companion is a late A-type dwarf (Teff=7900+/-200K; logg=4.3+/-0.2; M=1.7+/-0.1M_{sun}; R=1.7+/-0.2R{sun}) at a distance of 1.11+/-0.03kpc. No double-lined feature can be seen from the Gran Telescopio Canarias/HORuS high-resolution spectra; thus the radial-velocity variation indicates an invisible object hiding in the binary. The system's optical light curves show clear ellipsoidal variability, suggesting that the visible companion is tidal distorted. By fitting the multiband light curves with the eclipsing light-curve (ELC) code and the Wilson-Devinney (WD) code, we constrain the mass of the invisible star to be 1.1-1.3M{sun}_. Spectral disentangling shows no additional component with optical absorption spectra, supporting the idea that the system contains one compact object. No X-ray or UV emission is detected in the ROSAT archive observations. Therefore, we suspect the invisible object is more likely a neutron star rather than a white dwarf. Our finding suggests the ability of LAMOST spectroscopic survey to discover X-ray-quiescent compact objects.