  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 give 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 $\beta$-Bi$_{2}$Pd. 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 multi-class sheets.
The presence of soft phonon bands, in cooperation with the electron
susceptibility, account for electron-phonon superconductivity of single-layer
$\beta$-Bi$_{2}$Pd. With the centrosymmetric structure, single-layer
$\beta$-Bi$_{2}$Pd 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 monolayer candidate of
$\beta$-Bi$_{2}$Pd with intrinsic full-gap superconductivity.
