The pressure effects on atomic mean-square displacement, extended X-ray absorption fine structure (EXAFS) Debye-Waller factor and melting temperature of solid krypton have been investigated in within the statistical moment method scheme in quantum statistical mechanics. By assuming the interaction between atoms can be described by Buckingham potential, we performed the numerical calculations for krypton up to pressure 120 GPa. Our calculations show that the atomic mean-square displacement and EXAFS Debye-Waller factor of krypton crystal depend strongly on pressure. They make the robust reduction of the EXAFS peak height. Our results are in good and reasonable agreements with available experimental data. This approach gives us a relatively simple method for qualitatively calculating high-pressure thermo-physical properties of materials. Moreover, it can be used to verify future high-pressure experimental and theoretical works.