This study focuses on the stability and stabilization problems of a switching polynomial fuzzy system with a time-varying delay. The switching method is based on the operating sub-domains, and the switching polynomial Lyapunov function with a time-varying delay is used to design the switching polynomial static output feedback controller. The switching polynomial Lyapunov function contains a double-integral term for analyzing the upper bound of the time-varying delay. The stabilization of the polynomial system is investigated, using the boundary information of the membership functions and introducing slack polynomial matrices, which can reduce the conservatism of the stability conditions. Subsequently, the sum of squares conditions are obtained, which are convex and can be solved using SOSTOOLS. Finally, the viability and validity of the proposed approach are demonstrated using a numerical example.