Asteroseismology allows for deriving precise values of surface gravity of stars. The accurate asteroseismic determinations now available for large number of stars in the Kepler fields can be used to check and calibrate surface gravities that are currently being obtained spectroscopically for a huge numbers of stars targeted by large-scale spectroscopic surveys, such as the on-going Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Galactic survey. The LAMOST spectral surveys have obtained a large number of stellar spectra in the Kepler fields. Stellar atmospheric parameters of those stars have been determined with the LAMOST Stellar Parameter Pipeline at Peking University (LSP3), by template matching with the MILES empirical spectral library. In the current work, we compare surface gravities yielded by LSP3 with those of two asteroseismic samples - the largest sample from Huber et al. (2014) and the most accurate sample from Hekker et al. (2012, 2013). We find that LSP3 surface gravities are in good agreement with asteroseismic values of Hekker et al. (2012, 2013), with a dispersion of about 0.2 dex. Except for a few cases, asteroseismic surface gravities of Huber et al. (2014) and LSP3 spectroscopic values agree for a wide range of surface gravities. However, some patterns of differences can be identified upon close inspection. Potential ways to further improve the LSP3 spectroscopic estimation of stellar atmospheric parameters in the near future are briefly discussed. The effects of effective temperature and metallicity on asteroseismic determinations of surface gravities for giant stars are also discussed.