We study the classification and composite spectra of galaxies in the fourth data release (DR4) of the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST). We select 40182 spectra of galaxies from LAMOST DR4, which have photometric information but no spectroscopic observations in the Sloan Digital Sky Survey (SDSS). These newly observed spectra are recalibrated and classified into six classes - passive, H{alpha}-weak, star-forming, composite, LINER and Seyfert - using the line intensity (H{beta}, [OIII] 5007, H{alpha} and [NII] 6585). We also study the correlation between spectral class and morphological type through three parameters: concentration index, (u-r) colour and D4000n index. We calculate composite spectra of high signal-to-noise ratio (S/N) for six spectral classes and, using these composites, we pick out some features that can differentiate the classes effectively, including H{beta}, Fe5015, H{gamma}A, HK and the Mg2 band. In addition, we compare our composite spectra with the SDSS ones and analyse their differences. A galaxy catalogue of 40182 newly observed spectra (36601 targets) and the composite spectra of the six classes are available online (http://sciwiki.lamost.org/downloads/wll).