A conventional x-ray fluorescence computed tomography (XFCT) technique requires monochromatic synchrotron x-rays to simultaneously determine the spatial distribution and concentration of various elements such as metals in a sample. However, the synchrotron-based XFCT technique appears to be unsuitable for in vivo imaging under a typical laboratory setting. In this study we demonstrated, for the first time to our knowledge, the possibility of performing XFCT imaging of a small animal-sized object containing gold nanoparticles (GNPs) at relatively low concentrations using polychromatic diagnostic energy range x-rays. Specifically, we created a phantom made of polymethyl methacrylate plastic containing two cylindrical columns filled with saline solution at 1 and 2 wt% GNPs, respectively, mimicking tumors/organs within a small animal. XFCT scanning of the phantom was then performed using microfocus 110 kVp x-ray beam and cadmium telluride (CdTe) x-ray detector under a pencil beam geometry after proper filtering of the x-ray beam and collimation of the detector. The reconstructed images clearly identified the locations of the two GNP-filled columns with different contrast levels directly proportional to gold concentration levels. On the other hand, the current pencil-beam implementation of XFCT is not yet practical for routine in vivo imaging tasks with GNPs, especially in terms of scanning time. Nevertheless, with the use of multiple detectors and a limited number of projections, it may still be used to image some objects smaller than the current phantom size. The current investigation suggests several modification strategies of the current XFCT setup, such as the adoption of the quasi-monochromatic cone/fan x-ray beam and XFCT-specific spatial filters or pinhole detector collimators, in order to establish the ultimate feasibility of a bench-top XFCT system for GNP-based preclinical molecular imaging applications.