For the inverted catenary single-layer cylindrical reticulated shells with arch alignment in the form of catenary, the stability of three common grid configurations was analyzed and compared.A reasonable grid layout was determined, and the stability with single-layer cylindrical reticulated shells was compared. A large scale parameter analysis was carried out, including the effects of length-span ratio, raise-span ratio, member sectional dimension, initial geometric imperfection and unsymmetrical distribution of loads on the ultimate loads of the inverted catenary single-layer cylindrical reticulated shells. The results have shown that the slant rod of type I performs best overall stability capacity in the common grid configurations of inverted catenary single-layer cylindrical reticulated shells, and its stiffness and stability bearing capacity are greatly improved, compared with single-layer cylindrical reticulated shells. Raise-span ratio and length-span ratio influence the inverted catenary single-layer cylindrical reticulated shells significantly and have a good regularity, and the spacing of the structure transverse stiffening ribs should be less than the transverse width of the structure. Stability bearing capacity of the reticulated shells and section equivalent stiffness are in a linear relationship. The reticulated shells are proved to be sensitive to initial geometric imperfection when the initial imperfection value reaches 1/300 of the width, and the critical loads of the reticulated shells are maximally reduced by 57%. The reticulated shells are not sensitive to the asymmetric loads.