Terahertz time-domain spectroscopy is used as a new spectroscopic detection tool for the characterization of a wide range of substances including hydrates. Metal sulphates have a variety of different hydrates that exhibit different absorption properties in the terahertz band, and the different hydrates of transition metal sulphates can be effectively characterized by using terahertz spectroscopy. In this paper, magnesium sulphate and its hydrates were characterized by using a terahertz time-domain spectroscopy system. Different magnesium sulphate pyrolysis products were obtained by constant temperature drying of magnesium sulphate heptahydrate and their terahertz absorption spectra were investigated, which shows that different hydrates exhibit significantly different terahertz absorption properties. The research provides a simple, fast and effective means of characterization for the detection of magnesium sulphate and its hydrates, as well as an important reference for a variety of applications of magnesium sulphate.