The crystal structure of EuFe(2)As(2) has been studied up to a pressure of 35 GPa and down to a temperature of 8 K using temperature dependent x-ray diffraction in a diamond anvil cell at a synchrotron source. At 4.3 GPa, we have detected a structural phase transition from a high temperature tetragonal phase with I4/mmm space group to a low temperature orthorhombic phase with Fmmm space group around 120 K. With the application of pressure at a low temperature of 10 K, the orthorhombic phase is suppressed and a phase change to a collapsed tetragonal phase with I4/mmm space group is observed at 11 GPa. This collapsed tetragonal phase is similar to the one observed at ambient temperature and pressure above 8.5 GPa. We have shown that the collapsed tetragonal phase of EuFe(2)As(2) has the same pressure-volume (P-V) equation of state at ambient temperature and at 10 K, implying that the high pressure phase of EuFe(2)As(2) has a negligible thermal expansion coefficient.