To explore the strong coupling between the combined plasmonic mode supported by the metal nanoparticle and the anapole mode of the dielectric nanoparticle, a hybrid metal–dielectric nanoparticle consisting of the combination of silicon and silica together with the gold dimer is designed and analyzed by the finite element method (FEM). Theoretical simulation reveals that the enhanced electric field enhancement reaches 640 and unidirectional scattering with almost zero backscattering at multiple wavelengths is achieved in the far-field region. Moreover, the calculated Purcell factor of 12,193 and sensitivity of 610nm/RIU of the composite nanoparticle are much higher than those of the single-metal or dielectric nanoparticles. In the end, the impact of different structural parameters on the sensitivity, figure of merit and quality factor is analyzed and described, and the maximum sensitivity, Figure of merit and quality factor are found to be 2360nm/RIU, 18.4 RIU−1−1 and 19.8 RIU−1−1. The results reveal a new strategy to develop devices for surface-enhancement Raman scattering (SERS), quantum emitters, and sensors.