  We report the observation by angle-resolved photoemission spectroscopy
measurements of a highly anisotropic Dirac-cone structure in high quality
SrMnBi2 crystals. We reveal a well-defined sharp quasi-particle, linearly
dispersive with $v_{F_1}/v_{F_2}\sim$ 5--6, forming a hole-like anisotropic
Dirac-cone. The density of states for the cone remains linear up to as high as
~650 meV of binding energy. The scattering rate of the quasi-particle (QP)
increases linearly as function of binding energy, indicating a non-Fermi-Liquid
behavior. Our results suggest the existence of a dilute two-dimensional
electron gas system in this three-dimensional material.
