Metasurfaces consisting of hybrid metal/dielectric nanostructures carry advantages of both material platforms. The hybrid structures can not only confine electromagnetic fields in subwavelength regions, but they may also lower the absorption losses. Such optical characteristics are difficult to realize in metamaterials with only metal or dielectric structures. Hybrid designs also expand the scope of material choices and the types of optical modes that can be excited in a metasurface, thereby allowing novel light matter interactions. Here, we present a metallo-dielectric hybrid metasurface design consisting of a high-index dielectric (silicon) nanodisk array on top of a metal layer (aluminum) separated by a buffer oxide (silica) layer. The dimensions of Si nanodisks are tuned to support anapole states and the period of the nanodisk array is designed to excite surface plasmon polariton (SPP) at the metal-buffer oxide interface. The physical dimensions of the Si nanodisk and the array periods are optimized to excite the anapole and the SPP at normal incidence of light in the visible-NIR (400-900 nm) wavelength range. Finite difference time domain (FDTD) simulations show that, when the nanodisk grating is placed at a specific height (∼200 nm) from the metal surface, the two modes strongly couple at zero detuning of the resonances. The strong coupling is evident from the avoided crossing of the modes observed in the reflectance spectra and in the spectral profile of light absorption inside the Si nanodisk. A vacuum Rabi splitting of up to ∼ 129 meV is achievable by optimizing the diameters of Si nanodisk and the nanodisk array grating period. The proposed metasurface design is promising to realize open cavity strongly coupled optical systems operating at room temperatures.