Topological insulators are a recently discovered class of materials having insulating bulk electronic states but conducting boundary states distinguished by nontrivial topology. So far, several generations of topological insulators have been theoretically predicted and experimentally confirmed, all based on inorganic materials. Here, based on first-principles calculations, we predict a family of two-dimensional organic topological insulators made of organometallic lattices. Designed by assembling molecular building blocks of triphenyl-metal compounds with strong spin-orbit coupling into a hexagonal lattice, this new classes of organic topological insulators are shown to exhibit nontrivial topological edge states that are robust against significant lattice strain. We envision that organic topological insulators will greatly broaden the scientific and technological impact of topological insulators.