Detection angle is closely related to background noise, detection sensitivity, signal-to-noise ratio, and other parameters in the study of tube-excited X-ray fluorescence computed tomography (XFCT) imaging. Accordingly, we simulate a polychromatic tube-excited XFCT imaging system with multi-pinhole collimator using Geant4 to investigate the effect of detection angle on the signal-to-noise ratio and the reconstructed image quality. By changing the tube voltage, mass fraction of gold nanometer solution, and diameter of the region of interest, the signal-to-noise ratio is calculated by simulating the detection processes of the X-ray fluorescence projection data and scattering noise at four angles: 60°, 90°, 120°, and 150°. The simulation results reveal that the signal-to-noise ratio and reconstructed image quality could be effectively improved by increasing the detection angle. For most circumstances, the highest signal-to-noise ratio could be obtained when the detection angle is set to 120°.