We study the classification and composite spectra of galaxy in the fourth data release (DR4) of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). We select 40,182 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 re-calibrated and classified into six classes, i.e. passive, Hα-weak, star-forming, composite, LINER and Seyfert using the line intensity (Hβ, [OIII]λ5007, Hα and [NII]λ6585). We also study the correlation between spectral classes and morphological types through three parameters: concentration index, (ur) color, and D4000 n 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 Hβ, Fe5015, Hγ A , HK, and Mg 2 band etc. In addition, we compare our composite spectra with the SDSS ones and analyse their difference. A galaxy catalogue of 40,182 newly observed spectra (36,601 targets) and the composite spectra of the six classes are available online.