A Thomson scattering X-ray source can provide quasi-monochromatic, continuously energy-tunable, polarization-controllable and high-brightness X-rays, which makes it an excellent tool for X-ray fluorescence computed tomography (XFCT). In this paper, we examined the suppression of Compton scattering background in XFCT using the linearly polarized X-rays and the implementation feasibility of linearly polarized XFCT based on this type of light source, concerning the influence of phantom attenuation and the sampling strategy, its advantage over K-edge subtraction computed tomography (CT), the imaging time, and the potential pulse pile-up effect by Monte Carlo simulations. A fan beam and pinhole collimator geometry were adopted in the simulation and the phantom was a polymethyl methacrylate cylinder inside which were gadolinium (Gd)-loaded water solutions with Gd concentrations ranging from 0.2 to 4.0 wt%. Compared with the case of vertical polarization, Compton scattering was suppressed by about 1.6 times using horizontal polarization. An accurate image of the Gd-containing phantom was successfully reconstructed with both spatial and quantitative identification, and good linearity between the reconstructed value and the Gd concentration was verified. When the attenuation effect cannot be neglected, one full cycle (360°) sampling and the attenuation correction became necessary. Compared with the results of K-edge subtraction CT, the contrast-to-noise ratio values of XFCT were improved by 2.03 and 1.04 times at low Gd concentrations of 0.2 and 0.5 wt%, respectively. When the flux of a Thomson scattering light source reaches 1013 photons s-1, it is possible to finish the data acquisition of XFCT at the minute or second level without introducing pulse pile-up effects.