High-pressure angle-dispersive X-ray diffraction experiments on iron-based superconductor Ce(O0.84F0.16)FeAs were performed up to 54.9 GPa at room temperature. A tetragonal to tetragonal isostructural phase transition starts at about 13.9 GPa, and a new high-pressure phase has been found above 33.8 GPa. At pressures above 19.9 GPa, Ce(O0.84F0.16)FeAs completely transforms to a high-pressure tetragonal phase, which remains in the same tetragonal structure with a larger a-axis and smaller c-axis than those of the low-pressure tetragonal phase. The structure analysis shows a discontinuity in the pressure dependences of the Fe-As and Ce-(O, F) bond distances, as well as the As-Fe-As and Ce-(O, F)-Ce bond angles in the transition region, which correlates with the change in T-c of this compound upon compression. The isostructural phase transition in Ce(O0.84F0.16)FeAs leads to a drastic drop in the superconducting transition temperature T-c and restricts the superconductivity at low temperature. For the 1111-type iron-based superconductors, the structure evolution and following superconductivity changes under compression are related to the radius of lanthanide cations in the charge reservoir layer.