This paper studies the problem of sound propagation above a finite impedance plane. For this purpose, a spherical wave based half-space transfer function with velocity is derived and then is applied in the equivalent source method (ESM) to consider the influence of reflections caused by the finite impedance plane. With the half-space transfer function matching the surface velocity to the equivalent sources, the ESM is applied to estimate the sound filed above a finite impedance plane. Through two numerical simulation experiments, in which two vibrating objects, e.g., an oscillating sphere and a simply supported plate, are respectively used, the proposed model is examined. The results validate that the proposed model is feasible and effective to estimate the sound field above a finite impedance plane.