Additively manufactured gyroid structures have great potential in lightweight structure design, energy absorption, heat transfer, and biomedical applications. The optimization and design of the relative density of gyroid structures have been studied for a decade but mainly focusing on a single material phase. Multi-material Additive Manufacturing brought out the material complexity in structures, which extended the design parameter for gyroid structures from relative density to material distribution. In this research, a data-driven inverse design model was developed for multi-material gyroid structures using machine learning. The structures were fabricated by the material extrusion process with a combination of PLA and TPU materials. The mechanical properties of these structures were studied by compression tests and polynomial interpolations. It was found that the interpolation method can accurately indicate the relationship between relative density, material ratio, and mechanical properties. The interpolation functions were used to randomly generate the training data for machine learning. A well-trained neural network model was developed to find the inverse relationship between the mechanical properties and the design parameters. It is used in the design process to determine the relative density and PLA/TPU ratio by the elastic modulus, energy absorption, and peak stress. Subsequent validation experiments verified the efficacy of the proposed design model, demonstrating its ability to accurately predict the desired properties using the machine learning framework. Consequently, this innovative approach has substantially reduced the complexities associated with designing multi-material gyroid structures.