We perform a discrimination procedure with the spectral index diagram of TiO_5_ and CaH_2_+CaH_3_ to separate M giants from M dwarfs. Using the M giant spectra identified from LAMOST DR1 with high signal-to-noise ratio, we have successfully assembled a set of M giant templates, which show more reliable spectral features. Combining with the M dwarf/subdwarf templates in Zhong et al. (2015AJ....150...42Z, Cat. J/AJ/150/42), we present an extended library of M-type templates which includes not only M dwarfs with a well-defined temperature and metallicity grid but also M giants with subtypes from M0 to M6. Then, the template-fitting algorithm is used to automatically identify and classify M giant stars from LAMOST DR1. The resulting catalog of M giant stars is cross-matched with 2MASS JHKs and WISE W1/W2 infrared photometry. In addition, we calculated the heliocentric radial velocity of all M giant stars by using the cross-correlation method with the template spectrum in a zero-velocity rest frame. Using the relationship between the absolute infrared magnitude MJ and our classified spectroscopic subtype, we derived the spectroscopic distance of M giants with uncertainties of about 40%. A catalog of 8639 M giants is provided. As an additional result of this analysis, we also present a catalog of 101690 M dwarfs/subdwarfs which are processed by our classification pipeline.