High quality products are demanded due to increasingly fierce market competition. In this paper, the generation of surface wrinkle defect of welding wire steel ER70S-6 was studied by the combination of the experimental method and finite element simulation. Firstly, a thermal compression test was conducted on the Gleeble-3500 thermosimulator under different strain rates and temperatures and a strain dependent Arrhenius-type constitutive function was employed to fit the flow stress–strain curves obtained from the experiments. Then, the elastoplastic constitutive relationship was implemented using radial return mapping algorithm by means of the user subroutine VUMAT of Abaqus/Explicit. A new instability criterion was proposed to predict the possibility of the surface wrinkle defect during the multipass hot bar rolling process. In order to verify the reliability of the finite element model of the six-pass continuous rolling process, the simulated results were compared with experimental data. Finally, the effects of groove width and groove radius on the billet were investigated by the orthogonal test method, and the friction coefficient and rolling temperature. The results show that the groove width and groove radius are key factors to suppress the surface wrinkle defect. Decreasing the groove width can be beneficial for improving the surface quality and reducing the fillet radius. The optimized combination of the rolling process parameters was further applied in an industrial test and the surface quality of the billet was greatly improved.