In this paper, we investigate a light-confinement phenomenon in the structure which has triangular latice composed of Double NeGative Metamaterial (DNGM). In geometrical optics consideration, this structure is expected to confine lights completely by sequential refractions in the structure. We demonstrate it by using the two dimensional finite-difference time-domain simulations. We introduce Drude-Lorentz model for dielectric and magnetic dispersion of the material at optical frequencies. We analyze quantitatively the effects of energy loss in the DNGM on the light-confinement efficiency.