For the single-layer intersected inverted catenary cylindrical reticulated shell, the static properties and stability of the structures with different types of grid were studied and compared, and then the optimal grid form was obtained. The static properties and stability of the single layer intersected inverted catenary cylindrical reticulated shell were compared with those of the intersected circular cylindrical reticulated shell. Moreover, the stability of the former was studied comprehensively, including the buckling modes and the effect of various parameters such as the member sectional area, initial geometric imperfection, asymmetric load distribution, and support conditions on the ultimate load-carrying capacity. The results show that the structural performance of the single-layer intersected inverted catenary cylindrical reticulated shell with triangular grids is markedly superior to the circular one. Because, this kind of reticulated shell is sensitive to initial geometric imperfection, 1/300 of the structural span should be considered as the initial geometric imperfection value in the calculation of the ultimate load-carrying capacity. Additionally, the reticulated shell is also quite sensitive to the asymmetric load distribution, and the optimal value of rise-span ratio is 0.50 for shell stability.