Design optimization of structure and control combined systems are coupled problems. The conventional sequential design strategy (structure design sequentially followed by control design) usually neglects the coupling effects between structure and control and can only produce sub-optimal designs of the complex systems. Nevertheless, simultaneous design strategy with a reasonable and explicit optimization iteration management can ensure global optimization designs of the coupled system. In this study, a surrogate based co-design is explored to achieve the simultaneous optimization, which transforms continuous optimal control problems into discrete nonlinear programming problems. The discrete control parameters combining with the structure parameters can be simultaneously optimized and the co-design strategy can be achieved by introducing necessary and reasonable dynamic constraints. Here, the proposed surrogate based co-design is tested using a practical engineering case study, a heavy-load face-shovel excavator (FSE). The case study is built upon existing FSE design problems by incorporating detailed structure and control design variables while satisfying the system dynamic equations. The proposed surrogate based co-design is implemented and compared with the conventional sequential design strategy and an existing co-design strategy. Results indicate that the surrogate based co-design is accurate and efficient enough to achieve better performances than the conventional sequential design strategy by making FSE's structure more compact with relatively small vibrations.