We propose a pinhole-based fluorescent x-ray computed tomography (p-FXCT) system with a 2-D detector and volumetric beam that can suppress the quality deterioration caused by scatter components. In the corresponding p-FXCT technique, projections are acquired at individual incident energies just above and below the K-edge of the imaged trace element; then, reconstruction is performed based on the two sets of projections using a maximum likelihood expectation maximization algorithm that incorporates the scatter components. We constructed a p-FXCT imaging system and performed a preliminary experiment using a physical phantom and an I imaging agent. The proposed dual-energy p-FXCT improved the contrast-to-noise ratio by a factor of more than 2.5 compared to that attainable using mono-energetic p-FXCT for a 0.3 mg/ml I solution. We also imaged an excised rat's liver infused with a Ba contrast agent to demonstrate the feasibility of imaging a biological sample.