The recent discovery of infinite-layer nickel oxide superconductors has highlighted the importance of first-principles simulations. We predict an infinite-layer bismuth oxide superconductor BaBiO2, which is isostructural to NdNiO2. In this work, electronic structure, lattice dynamics, and electron–phonon interaction are studied, with special attention paid to the influence of spin–orbit coupling (SOC) on the above-mentioned quantities. Our calculations show that the structure will be dynamically stable under pressure and induce superconductivity, whether SOC is considered or not. In addition, SOC will significantly enhance the electron–phonon coupling (EPC), resulting in an increase in EPC constant λ from 0.43 to 0.73. We further find that the Fermi surface nesting is partially responsible for its superconductivity. A strong SOC changes the Fermi surface and enhances the nesting, and the EPC becomes stronger. Our results propose a bismuth-based superconductor, demonstrating the importance of SOC for its superconductivity and providing clues for further experimental synthesis.