The crystal structure and electrical resistance of the structurally-layered EuFe2As2 have been studied up to 70 GPa and down to temperature of 10 K, using a synchrotron x-ray source and the designer diamond anvils. The room-temperature compression of the tetragonal phase of EuFe2As2 (I4/mmm) results in an increase in the a-axis and a rapid decrease in c-axis with increasing pressure. This anomalous compression reaches a maximum at 8 GPa and the tetragonal lattice behaves normal above 10 GPa with a nearly constant c/a axial ratio. The rapid rise in superconducting transition temperature (Tc) to 41 K with increasing pressure is correlated to this anomalous compression and a decrease in Tc is observed above 10 GPa. We present P-V data or equation of state of EuFe2As2 in both the ambient tetragonal phase and the high pressure collapsed tetragonal phase to 70 GPa.