Electronic energy bands of the Tl-based ternary chalcogenide TlGaTe₂ with a quasi one-dimensional crystalline structure have been studied by means of high resolution angle-resolved photoemission spectroscopy (ARPES) in order to check for dispersive structures similar to the Dirac cone observed in the surface bands of Bi-based binary chalcogenides. Two linear dispersive structures which are not reproduced in band calculations for bulk material have been observed in the energy band along the Γ–N direction perpendicular to the chains. These dispersions form a cross-type structure that is centered at the Γ point and extends along the Γ–H–T direction parallel to the chains, reflecting, in our opinion, one-dimensional features of surface morphology of TlGaTe₂. The cross-type structure, the energy position of which linearly varies with excitation photon energy, is observed only for high-grade quality surfaces of TlGaTe₂. It is therefore assumed that the observed peculiar dispersive structure is caused by the Dirac-type dispersion of high-lying surface conduction bands and that ARPES detects the joint density of states.