Anisotropic superconductivity in the two-dimensional metal-organic kagome framework <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Cu</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:

Motivated by the theoretical prediction of superconductivity in the ${\mathrm{Cu}}_{3}{(\mathrm{CS})}_{6}$ monolayer and the successful experimental realization of its analogous oxygen counterpart ${\mathrm{Cu}}_{3}{(\mathrm{CO})}_{6}$ monolayer [X. Zhang et al., Nano Lett. 17, 6166 (2017); R. Zhang et al., Angew. Chem. 132, 2691 (2020); N. Shaiek et al., Adv. Mater. Interfaces 9, 2201099 (2022)], we present a comprehensive theoretical investigation of phonons and the electron-phonon coupling mechanism in the ${\mathrm{Cu}}_{3}{(\mathrm{CO})}_{6}$ monolayer. Our first-principles calculations reveal that this well-defined two-dimensional metal-organic framework (2D-MOF) is a superconductor with a critical temperature of 16.5 K. This robust superconductivity is driven by a strong electron-phonon coupling ($\ensuremath{\lambda}=0.72$), predominantly contributed by the strong interaction between low-energy phonons (dominated by Cu and O atoms) and electronic states (formed by Cu ${d}_{xy,{x}^{2}\ensuremath{-}{y}^{2}}$ and O $s+{p}_{x,y}$ orbitals) near the Fermi level. Furthermore, we find that ${\mathrm{Cu}}_{3}{(\mathrm{CO})}_{6}$ monolayer exhibits a Bardeen-Cooper-Schrieffer superconducting state characterized by a single anisotropic gap. Our findings in 2D-MOFs highlight the great potential for exploring superconductivity in this promising class of materials.