We examine the electronic and magnetic structures of iron telluride KFe₂Te₂ using first-principle calculations. We demonstrate that the ground state of this compound is in bicollinear antiferromagnetic order with Fe local moments (~ 2.6 μ_B) that are ferromagnetically aligned along a diagonal direction and antiferromagnetically aligned along the other diagonal in the Fe-Fe square lattice, similar to the alignment discovered in the parent compound of superconductor α-FeTe. This bicollinear antiferromagnetic order results from the interplay among the nearest, next-nearest, and next-nextnearest neighbor exchange interactions, which are mediated by Te 5p orbitals. This finding may aid our understanding of the interplay between magnetism and superconductivity in the family of iron-based materials.