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Innovative design of complex systems faces multi-contradiction (MC). The existing methods to solve MC are mainly based on the General Theory of Powerful Thinking (OTSM) which is independent of the classical Engineering Design Method (ED) to form the process model, they cannot inherit the accumulated knowledge and advantages of ED. This paper proposes a product innovation design process model for MC based on the function-structure model. It starts with an initial scenario of the system to build the function-structure model and MC network based on the root contradiction analysis. The network structure entropy and function importance decision methods are introduced for the trimming target confirming. The key contradiction-node is identified and solved by strategies of trimming based on internal and external resources of the system. The function-structure model in ED and trimming in TRIZ are combined to form an innovative design process for MC systems. The proposed method is evaluated in a case study of an innovative design of the girder bridge erector. [ABSTRACT FROM AUTHOR]