The phonon thermal conductivity of Gallium nitride (GaN) nanofilms and nanowires under prestress fields are investigated theoretically. In the framework of elasticity theory, the phonon dispersion relations of spatially confined GaN nanostructures are achieved for different phonon modes. The acoustoelastic effects stemmed from the preexisting stresses are taken into account in simulating the phonon properties and thermal conductivity. Our theoretical results show that the prestress fields can alter the phonon properties such as the phonon dispersion relation and phonon group velocity dramatically, leading to the change of thermal conductivity in GaN nanostructures. The phonon thermal conductivity is able to be enhanced or reduced through controlling the directions of prestress fields operated on the GaN nanofilms and nanowires. In addition, the temperature and size-dependence of thermal conductivity of GaN nanostructures will be sensitive to the direction and strength of those prestress fields. This work will be helpful in controlling the phonon thermal conductivity based on the strain/stress engineering in GaN nanostructures-based electronic devices and systems.