In order to develop the fabrication technology of GaP nanowires (NWs) integrated with Au nanoparticles (NPs), i.e., of an object promising for creating red-range micro-LEDs, its light extraction efficiency has been analyzed both with and without the Au NP. Moreover, the relationship between this efficiency and the position of the active region within the core-shell LED heterostructure was investigated. In this case the full-wave optical numerical simulation of light propagation using the "COMSOL Multiphysics" software package, specifically the "Wave Optics" module, was performed. The system under study included a silicon substrate in the aerial environment with the object (GaP NW + Au NP) clamped to. An imitation of an optical point dipole was taken as a radiation source. The presence of the Au nanoparticle was shown to lead to a significant increase (of approximately 12%) in light extraction efficiency due to localized surface plasmon resonance and the enhancement of the near electric field in the contact area of the Au particle with the nanocrystal.