About 766 delta Scuti stars were observed by LAMOST by 2017 June 16. Stellar atmospheric parameters of 525 variables were determined, while spectral types were obtained for all samples. In the paper, those spectroscopic data are catalogued. We detect a group of unusual and cool variable stars (UCVs) that are distinguished from the normal delta Scuti stars (NDSTs). On the H-R diagram and the log g-T diagram, the UCVs are far beyond the red edge of pulsational instability trip. Their effective temperatures are lower than 6700 K with periods in the range from 0.09 to 0.22 d. NDSTs have metallicity close to that of the Sun as expected, while UCVs are slightly metal poor than NDSTs. The two peaks on the distributions of the period and stellar atmospheric parameters are all caused by the existence of UCVs. When those UCVs are excluded, it is discovered that the effective temperature, the gravitational acceleration, and the metallicity all are correlated with the pulsating period for NDSTs and their physical properties and evolutionary states are discussed. Detection of those UCVs indicates that about 25 per cent of the known delta Scuti stars may be misclassified. However, if some of them are confirmed to be pulsating stars, they will be a new-type pulsator and their investigations will shed light on theoretical instability domains and on the theories of interacting between the pulsation and the convection of solar-type stars. Meanwhile, 88 delta Scuti stars are detected to be the candidates of binary or multiple systems.