  Two-dimensional (2D) topological superconductors are highly desired because
they not only offer opportunities for exploring novel exotic quantum physics,
but also possesses potential applications in quantum computation. However,
there are few reports on 2D superconductors, let alone topological
superconductors. Here, we find a 2D monolayer W$_2$N$_3$, which can be
exfoliated from its real van der Waals bulk material with much lower
exfoliation energy than MoS$_2$, to be a topological metal with exotic
topological states at different energy level. Due to the Van Hove
singularities, the density of states near Fermi level are high, making the
monolayer a compensate metal. Moreover, the monolayer W$_2$N$_3$ is unveiled to
be a superconductor with the superconducting transition temperature Tc $\sim$
22 K and a superconducting gap of about 5 meV based on the anisotropic
Migdal-Eliashberg formalism, arising from the strong electron-phonon coupling
around the $\Gamma$ point. Because of the strong electron and lattice coupling,
the monolayer displays a non-Fermi liquid behavior in its normal states at
temperatures lower than 80 K, where the specific heat exhibit T$^3$ behavior
and the Wiedemann-Franz law dramatically violates. Our findings not only
provide the platform to study the emergent phenomena in 2D topological
superconductors, but also open a door to discover more 2D high-temperature
topological superconductors in van der Waals materials.
