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.
