Two-dimensional X-ray inspection systems are widely used in aviation security applications; however, they have inherent limitations in recognizing the three-dimensional (3D) shapes of hidden objects. Therefore, there is a growing demand for the implementation of advanced 3D X-ray inspection systems at airports for more accurate detection of threats in luggage and personal belongings. In this study, we designed a new stationary computed tomography (CT) baggage scanner with π-angle sparsity (i.e., 20 pairs of X-ray sources and line detectors were placed within a scan angle of 180°) and compressed sensing (CS)-based reconstruction, and implemented a dual-energy material decomposition (DEMD) technique in the proposed system to separate soft and dense materials of an examined object to enhance threat detection. To validate the efficacy of the proposed approach (CS/180°/P20), we conducted a feasibility study using numerical simulation before its practical implementation. Polychromatic projections were emulated at X-ray tube voltages of 60 and 140 kVp, and DEMD was applied to the projections prior to CT reconstruction. Conventional and dual-energy CT images were reconstructed using both standard filtered-backprojection (FBP) and state-of-the-art CS-based algorithms to compare the image quality. According to our simulation results, the CS-reconstructed images were almost unaffected by the clearly evident streak artifacts on the FBP-reconstructed images because of the use of 20 extreme sparse-view projections, and the image quality of the dual-energy CT images obtained using the proposed CT configuration was similar to that obtained using the conventional CT configuration with 720 dense projections, indicating the efficacy of the proposed approach. Consequently, high-quality dual-energy CT images of soft and dense materials were successfully obtained using the proposed stationary CT configuration.