Abstract: Employing the semi-discretization in the scaled boundary finite element method (SBFEM) and the Higdon transmitting differential operators, an efficient discrete high-order Higdon-like transmitting boundary condition is proposed for scalar wave propagation in 2D layered media. Applying Galerkin finite element discretization along the boundary of unbounded medium, the partial differential equation for scalar waves is transformed into a semi-discrete matrix equation in the local coordinates. Then, employing the original Higdon boundary and auxiliary variables, a discrete high-order transmitting boundary condition is formulated in the time domain as a system of ordinary differential equations not involving any derivatives higher than the second order. It is temporally local and spatially non-local and can be solved by standard time-integration schemes. Numerical examples demonstrate that the accuracy of the discrete high-order transmitting boundary condition can be improved by increasing its order. As the number of operations increases linearly with the order, this method is more efficient than the convolution method. In addition, this transmitting boundary condition can be coupled straightforwardly with finite elements as it is expressed directly in nodal values on the boundary.