X-ray fluorescence computed tomography is a stimulated emission tomography that allows nondestructive reconstruction of the elements distribution in the sample, which is important for biomedical investigations. Owing to the high flux density and easy energy tunability of highly collimated synchrotron X-rays, it is possible to apply X-ray fluorescence CT to biomedical samples. Reported in the present paper, an X-ray fluorescence CT system was established at Shanghai Synchrotron Radiation Facility for the investigations of trace elements distribution inside biomedical samples. By optimizing the experiment setup, the spatial resolution was improved and the data acquisition process was obviously speeded up. The maximum-likelihood expectation-maximization algorithm was introduced for the image reconstruction, which remarkably improved the imaging accuracy of element distributions. The developed system was verified by the test sample and medical sample respectively. The results showed that the distribution of interested elements could be imaged correctly, and the spatial resolution of 150 m was achieved. In conclusion, the developed system could be applied to the research on large-size biomedical samples, concerning imaging accuracy, spatial resolution and data collection time.