An absorbing boundary condition (ABC) is particularly important for finite element simulation of wave propagation in a multilayered medium. In this paper, a spatially and temporally local high-order absorbing boundary condition is proposed for scalar wave propagation in semi-infinite multilayered media. A semi-discrete motion equation is derived by discretizing the truncation boundary of the semi-infinite domain along the vertical direction. The scalar dynamic stiffness in the frequency domain for a single degree of freedom (DOF) on the truncation boundary is obtained by only considering the first mode of the semi-infinite domain. The scalar dynamic stiffness is expressed as a continued fraction expansion that is stable and converges exponentially to the exact solution. The ABC based on the continued fraction for a single DOF on the truncation boundary is established by introducing auxiliary variables. The proposed ABC is always stable and it can be coupled straightforwardly with the existing finite element method. Since it is spatially decoupled and the coefficients in it are easy to obtain, the proposed ABC is convenient to apply in engineering. Numerical examples demonstrate the superior properties of the proposed method with high accuracy, high efficiency, and good stability.