All-dielectric optical metasurfaces that supporting optical quasibound states in the continuum (QBICs) offer a promising platform in realization of strong light-matter coupling with monolayer transition-metal dichalcogenides (TMDCs). Such coupled systems are critical for wide range of applications in low-dimensional polaritonic physics, optoelectronic and valleytronic devices. Here, we propose a strongly coupled system between Brillouin zone folding driven quasibound states in the continuum (BZF-QBIC) mode of high-index GaP metasurfaces and excitons of monolayer $\mathrm{W}{\mathrm{S}}_2$. By changing the height of the GaP metasurface, we observe a typical anticrossing behavior with a Rabi splitting of 38.2 meV. Simulations also show that the coupling strength is strongly dependent on both the localized electric field enhancement of the metasurface and the linewidth of the BZF-QBIC mode, there is a balance between these two factors for maximizing the coupling effect. Unlike the existing QBIC mode whose resonant wavelength is sensitive to the asymmetric parameter of the dielectric metasurface, BZF-QBICs mode exhibits an asymmetric perturbation-near-independent resonant behavior simultaneously with a high-quality factor, making it ideal for achieving strong coupling in monolayer TMDCs. This work provides a strategy for realizing monolayer TMDCs-assisted strong coupling, and facilitates potential applications in low-dimensional polaritonic devices.

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• Exciton polariton
• Metasurfaces
• Surface plasmon polariton
• Transition metal dichalcogenides