Abstract: A kind of gray-scale logic OR operation (GLOGOR) CNN was proposed by formulating the logic OR algorithms for gray-scale images. It could perform a pixel-wise logic OR operation on corresponding elements of two gray-scale images. A theorem was established to design the robustness template parameters of GLOGOR CNN, and a rigorous mathematical proof was given. The theorem provided parameter inequalities for determining parameter intervals to implement the corresponding tasks. The simulation results illustrate the effectiveness of the methodology.