A spectral computed tomography (CT) system based on an energy-resolved photon-counting Cadmium Zinc Telluride (CZT) detector with a dual energy technique can provide spectral information and can possibly distinguish between two or more materials with a single X-ray exposure using energy thresholds. This work provides the potential for three-material decomposition of vulnerable plaques using two inverse fitting functions. Additionally, there exists the possibility of using gold nanoparticles as a contrast agent for the spectral CT system in conjunction with a CZT photon-counting detector. In this simulation study, we used fan beam CT geometry that consisted of a 90 kVp X-ray spectrum and performed calculations by using the SpekCal program (REAL Software, Inc.) with Monte Carlo simulations. A basic test phantom was imaged with the spectral CT system for the calibration and decomposition process. This phantom contained three different materials, including lipid, iodine and gold nanoparticles, with six holes 3 mm in diameter. In addition to reducing pile-up and charge sharing effect, the photon counting detector was considered an ideal detector. Then, the accuracy of material decomposition techniques with two inverse fitting functions were evaluated between decomposed images and reference images in terms of root mean square error (RMSE). The results showed that decomposed images had a good volumetric fraction for each material, and the RMSE between the measured and true volumes of lipid, iodine and gold nanoparticle fractions varied from 12.51% to 1.29% for inverse fitting functions. The study indicated that spectral CT in conjunction with a CZT photon-counting detector in conjunction with a dual energy technique can be used to identifying materials and may be a promising modality for quantifying material properties of vulnerable plaques.