An in situ high pressure study using energy dispersive X-ray diffraction has been carried out on the polycrystalline high-Tc superconductor, HgBa2CuO4+δ (Hg-1201), to study its phase stability under pressure and also to measure its compressibility and bulk modulus. No evidence of pressure-induced polymorphism was found in the pressure range investigated, i.e., from 0.1 MPa (1 atm) to 5 GPa. The compound exhibited anisotropic elastic properties. The axial compressibility along the c axis was measured to be (3.96±0.35)×10−3GPa−1 and along the a axis (3.42±0.13)×10−3GPa−1, corresponding to an anisotropy ratio of 1.16±0.11. The bulk modulus was determined to be (94.7±4.2) GPa and, assuming a Poisson's ratio of 0.2, Young's modulus was estimated to be (170±8) GPa.