We have investigated structural and magnetic phase transitions under high pressures in a quaternary rare earth transition metal arsenide oxide NdCoAsO compound that is isostructural to high temperature superconductor NdFeAsO. Four-probe electrical resistance measurements carried out in a designer diamond anvil cell show that the ferromagnetic Curie temperature and anti-ferromagnetic Neel temperature increase with an increase in pressure. High pressure x-ray diffraction studies using a synchrotron source show a structural phase transition from a tetragonal phase to a new crystallographic phase at a pressure of 23 GPa at 300 K. The NdCoAsO sample remained anti-ferromagnetic and non-superconducting to temperatures down to 10 K and to the highest pressure achieved in this experiment of 53 GPa. A P-T phase diagram for NdCoAsO is presented to a pressure of 53 GPa and low temperatures of 10 K.