With the advantage of high strength, lightness, and good environmental resistance, glass fiber reinforced polymer (GFRP) pultruded profile is regarded as an innovative way that has been used in infrastructure over the last few decades. However, some disadvantages also limited its widespread application in practice, including relatively low elastic and shear modulus and high deformability due to buckling failure. To overcome these disadvantages, some composite structure systems are proposed, such as GFRP-concrete composite structure system. This paper presents an innovative GFRP-concrete composite bridge prototype system, which mainly includes two I-shaped GFRP girders with corrugated webs combined with a thin steel fiber reinforced self-compacting concrete (SFRCC) deck. This composite bridge system is proved to improve structure shear stability and bending stiffness. Three-dimensional finite element (FEA) models are created to simulate the flexural behavior of two-I-shaped-girder composite bridge with straight webs, and the model result is validated with experimental data. Furthermore, the revised FE model that uses corrugated webs instead of straight webs is created, and the static and dynamic behaviors are investigated, including shearing stability properties, bending vibration frequency due to bending and torsion, mid-span vertical deflection, and lateral displacement due to wind load. Further research efforts on the influence of parameters dimension variation in corrugated webs girder composite system are needed. A total of four variable parameters are selected to test, which are GFRP corrugated web width, thickness, height, and SFRCC top slab thickness, respectively. All these conclusions will provide some design recommendations and guideline of a GFRP-concrete corrugated webs composite bridge in further study.