We predict theoretical existence of intrinsic two-dimensional organic topological insulator (OTI) states in Cu–dicyanoanthracene (DCA) lattice, a system that has also been grown experimentally on Cu substrate, based on first-principle density functional theory calculations. The p z -orbital Kagome bands having a Dirac point lying exactly at the Fermi level are found in the freestanding Cu–DCA lattice. The tight-binding model analysis, the calculated Chern numbers, and the semi-infinite Dirac edge states within the spin–orbit coupling gaps all confirm its intrinsic topological properties. The intrinsic TI states are found to originate from a proper number of electrons filling of the hybridized bands from Cu atomic and DCA molecular orbitals based on which similar lattices containing noble metal atoms (Au and Cu) and those molecules with two CN groups (DCA and cyanogens) are all predicted to be intrinsic OTIs.