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.
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