MgF₂ is an important member of alkaline-earth fluorides and has a wide range of applications in industry. Meanwhile, MgF₂ occurs naturally as a mineral sellaite. Compared with the study of its electronic structure and optical properties, the researches of the behavior under high pressure of MgF₂, especially the thermodynamic properties are still limited. The high-pressure melting, volume thermal expansion coefficient, and thermoelastic parameter of the Earth’s lower mantle mineral, like MgF₂, are of interest and importance for understanding the physical nature of the functional material and for recognizing the structural compositions, dynamics, evolution and origin of the earth. Using the first-principles calculations based on density functional theory, the thermodynamic, mechanical, and dynamic stability of the fluorite-type structure for MgF₂ are systematically studied. The calculations indicate that the fluorite-type structure is a high-pressure phase and it is stable at least up to 135 GPa. According to the principle of equal enthalpies, the phase transition pressure of MgF₂ crystal from stable rutile structure to high pressure fluorite structure is determined to be 19.26 GPa and 18.15 GPa based on the the generalized gradient approximation and local density approximation calculations, respectively. The high-temperature structural stability of MgF₂ with the fluorite-type structure is investigated and confirmed by using the classical molecular dynamics (MD) simulations by taking into account the molar volume and total energy change behavior in a temperature range from 300 to 6000 K. On the basis of previous research, the volume thermal expansion coefficient, isothermal bulk modulus, and thermoelastic parameter of MgF₂ with the CaF₂-type fluorite structure are predicted systematically in a temperature range from 300 to 1500 K and in a pressure range from 0 to 135 GPa with the help of the generalized gradient approximation of the revised Perdew-Burke-Ernzerhof form combined with quasiharmonic Debye model calculations and the molecular dynamics method combined with reliable interatomic potentials. An important discovery is that the thermoelastic parameter of this material under low temperature and low pressure is not a constant as assumed usually in previous studies of the equation of states, but it approaches to a constant under both high temperature and high pressure.