The detection angle within X-ray fluorescence computed tomography (XFCT) is closely related to fluorescence collecting efficiency. We design a multi-detection angle pencil-beam XFCT imaging system base on MCNP5 to simulate the imaging of a gold nano-solution columnar phantom with a mass concentration of 1%, and use filtered back projection (FBP) algorithm and joint simultaneous algebraic reconstruction technology (SART) and maximum likelihood expectation maximization (ML-EM) algorithm to reconstruct the element distribution. The contrast-to-noise ratio is calculated to quantitatively analyze reconstruction image quality with different algorithms at different angles. The results show that the FBP algorithm has better imaging quality at the backscatter angle. The SART algorithm and the ML-EM algorithm have better imaging quality at the vertical angle and the backscatter angle.