The compressibility and expansivity of anglesite (PbSO4) have been measured at high pressure up to 21.6 GPa and high temperature up to 700 K using in situ angle-dispersive X-ray diffraction and diamond anvil cell. The third-order Birch-Murnaghan equation of state (III-BM-EoS) was used to analyze the pressure-volume (P-V) data of PbSO4. We obtained the bulk modulus K-0 = 59(1) GPa, and its pressure derivative K-0' = 5.3(4), respectively. Using Holland-Powell thermal EoS to fit the temperature-volume (T-V) data, the thermal expansion coefficient alpha(0) = 4.59(2) x 10(-5) K-1 for PbSO4 was also derived. Simultaneously, the ambient-pressure axial compressibilities (beta(a0) = 1.79(4) x 10(-3) GPa(-1), beta(b0) = 1.75(5) x 10(-3) GPa(-1), beta(c0) = 2.12(4) x 10(-3) GPa(-1)) and axial thermal expansivities (alpha(a0) = 1.23(4) x 10(-5) K-1, alpha(b0) = 1.93(2) x 10(-5) K-1, and alpha(c0) = 1.43(1) x 10(-5) K-1) along a-axis, b-axis and c-axis were derived at 300 K, respectively. Furthermore, the potential influencing factors (e.g., the effective size of M2+ cation, polarizability and electronegativity) on the bulk moduli of barite-type (belonging to Pbnm space group) sulfates (anglesite, barite, and celestine) were discussed. We found that the polarizability might be the most important factor. Finally, the anisotropic linear compressibility and thermal expansivity in barite-type sulfates were also discussed, respectively.