The structural stability and elastic properties of celestine have been investigated at room temperature and pressure up to 15GPa, by using in situ angle-dispersive X-ray diffraction and a diamond anvil cell. No phase change is observed within the range of pressure in this study. Analysis of room temperature P-V data to a third-order Birch-Murnaghan (BM) Eos yields: the zero-pressure volume V-0 = 306.0(6) angstrom(3), isothermal bulk modulus K-0 = 62(5) GPa and its pressure derivative K'(0) = 11(1). If K'(0) is fixed at 4, then the isothermal bulk modulus is K-0 = 98(2) GPa. In addition, the axial compressiblity moduli of the three unit cell axes of celestine are obtained as K-a0 = 102(2) GPa, K-b0 = 92(2) GPa and K-c0 = 98(2) GPa, indicating the anisotropy of axial compressibility, with the a axis the most incompressible and the b axis the most compressible. Furthermore, the elastic properties of barite-type sulfates are discussed by combining the results in this study with previous studies on barite-group minerals.