Optical losses of chalcogenide negative curvature hollow-core fibers with hybrid cladding elements were numerically investigated in this study. Microstructured cladding formed by the combination of tubular and elliptical elements was designed for low-loss operation in the mid-infrared spectrum. A confinement loss value of 0.287 dB/km was calculated for the proposed ellipse-nested tubular negative curvature fiber with optimized design parameters at 10.6 µm. Achieved confinement losses with the proposed design are several orders of magnitude lower than the tubular/elliptical negative curvature fibers in the targeted spectrum. The effect of the material absorption to the total fiber losses was also investigated along with the confinement losses. Suppression on the higher-order modes by the proposed fiber was numerically observed. The negative curvature fibers are promising for the low-loss guidance of CO2 lasers that are widely used for various applications spanning from material processing to surgery.