The paper is devoted to develop a new scheme to calculate impedance matrices for axial-symmetric foundations embedded in half-space medium. The half-space medium can be approximated by increasing thickness of one layer stratum on rigid bedrock due to the effect of material damping. However, as thickness increases, the numerical problem will arise. This problem is caused by the numerical contamination by some negligible reflection waves from rigid bedrock. In reality, the effect of these reflection waves on impedance is getting small as the thickness of the one layer stratum increases. Therefore, the scheme will employ the solutions for one layer stratum with suppressing these reflection waves to generate the impedance for the case of half-space. The numerical results by the presented scheme are compared with the results by other scheme in order to show that the new numerical scheme is effective and the solutions in layered medium can be extended to obtain the results for the cases of layered half-space medium. Some numerical results of torsional, vertical, horizontal, coupling and rocking impedances with different embedded depths will be presented and comments on the numerical scheme will be given.