Abstract We present a systematic derivation of a minimal five-band tight-binding model for the description of the electronic structure of the recently discovered quasi-one-dimensional superconductor K₂Cr₃As₃. Taking as a reference the density-functional theory (DFT) calculation, we use the outcome of a Löwdin procedure to refine a Wannier projection and fully exploit the predominant weight at the Fermi level of the states having the same symmetry of the crystal structure. Such states are described in terms of five quasi-atomic d orbitals: four planar orbitals, two d _xy and two d x 2 − y 2 , and a single out-of-plane one, d z 2 . We show that this minimal model reproduces with great accuracy the DFT band structure in a broad energy window around the Fermi energy. Moreover, we derive an explicit simplified analytical expression of such model, which includes three nearest-neighbor (NN) hopping terms along the z direction and one NN term within the xy plane. This model captures very efficiently the energy spectrum of the system and, consequently, can be used to study transport properties, superconductivity and dynamical effects in this novel class of superconductors.