Topological　superconductors,　characterized　by　topologically　nontrivial　states　residing　in　a　superconducting　gap,　are　a　recently　discovered　class　of　materials　having　Majorana　fermions.　The　interplay　of　superconductivity　and　topological　states　gives　rise　to　opportunities　for　achieving　such　topological　superconductors　in　condensed　matter　systems.　Up　to　now,　several　single-material　topological　superconductors　in　this　form　have　been　theoretically　predicted　and　experimentally　confirmed.　Here,　using　the　first-principles　calculations,　we　study　the　superconducting　single-layer　β-Bi2Pd.　The　electronic　density　of　states　near　Fermi　level　of　this　monolayer　are　dominated　by　the　Bi-p　and　Pd-d　orbitals,　forming　a　two-band　Fermi　surface　with　multiclass　sheets.　The　presence　of　soft　phonon　bands,　in　cooperation　with　the　electron　susceptibility,　accounts　for　electron-phonon　superconductivity　of　single-layer　β-Bi2Pd.　With　the　centrosymmetric　structure,　single-layer　β-Bi2Pd　possesses　a　continuous　gap　over　the　whole　Brillouin　zone　and　topological　Dirac-like　states　at　its　one-dimensional　boundary.　The　present　findings　would　lead　to　the　expectation　of　one-dimensional　topological　superconductivity　and　Majorana　bound　states　in　a　monolayer　candidate　of　β-Bi2Pd　with　intrinsic　full-gap　superconductivity.　©　2020　American　Physical　Society.