Coded-aperture gamma imaging techniques have been applied widely in several radiation monitoring fields. However, in terms of the design of the coded-aperture mask, the category and rank of the mask are generally considered, but there is a lack of detailed research on selection of the appropriate mask thickness. Concretely, the imaging performance is affected by the mask thickness in terms of two factors: the full-field image quality of the overall field of view (FOV), which represents the background noise tolerance of the radioactive source; and the image brightness consistency, which represents consistency of the imaging efficiency. We have studied and analyzed these two imaging performance indexes in relation to the mask thickness based on the model of our custom-made gamma camera. Specifically, the full-field image quality initially improves and later deteriorates with the mask thickness increases from 0.1 mm to 30 mm because of the competition and the tradeoff between the transmission background and the oblique irradiation effect; the image brightness consistency initially descends, then improves, and finally decreases again under the same conditions as a result of the tradeoff between the improvement of the transmission background ratio and deterioration of the oblique irradiation coefficient ratio. Furthermore, these two indexes change trends are both related to gamma-ray energy. Finally, based on a comprehensive analysis of the imaging performance, the optimal thicknesses for the customized W-Cu alloy modified uniformly redundant array masks for 59.5 keV, 662 keV, 1250 keV gamma-ray imaging are 0.5 mm, 10 mm, and 16 mm, respectively.