This paper proposes a generalized multiple-scattering (GMS) method to evaluate the current distribution on a cable harness with ground connections to a nearby metal surface. The GMS method is a hybrid method combining the transmission line theory and the method of moments. The GMS method uses the generalized multiconductor transmission line (GMTL) solver for the cable harness part and the mixed-potential integral equation (MPIE) solver for the rest of the structure including the metal surface and the grounding wires. Neither the GMTL nor the MPIE solver alone takes into account the mutual interactions between the cable harness and the rest of the structure. Therefore, an iterative scheme is arranged in the GMS method to compensate the above-mentioned interactions. These interactions occur via not only field couplings, but also current conducting through the grounding points on the cable harness. A numerical test case is provided to benchmark the proposed GMS method.