The performance of a virtual (6 × 6 × 15 mm3) Frisch-grid cadmium zinc telluride detector for the detection of contraband with 14 MeV neutron-activation prompt γ-rays was studied using Monte Carlo simulations. A sensitive nonlinear iterative peak clipping algorithm was applied to the spectra to rapidly and easily identify the prompt γ-ray peaks. This algorithm showed better performance than directly using the original spectra. The CZT detector showed good energy resolution for the high energy prompt γ-rays and its carbon-to-oxygen peak ratios were almost equal to the theoretical value of the target contraband materials. The minimum detectable concentration of carbon and oxygen elements using the CZT detector was calculated. The simulation results for the CZT detector were compared to those of a HPGe detector and demonstrated the feasibility of using a CZT detector in neutron activation analysis.