The invention discloses a square rigid cable dome structure. Rigid members form mutually vertical grids and are positioned on a convex hyperboloid; boundary ring beams are arranged at the peripheries of the grids; vertical brace rods perpendicular to the ground are arranged under grid nodes of the rigid members on horizontal symmetric axes and vertical symmetric axes as well as grid nodes of the peripheral rigid members; oblique cords are connected between the network nodes of the horizontal symmetric axes and the vertical symmetric axes and the lower ends of the adjacent inside vertical brace rods; oblique cords are connected between nodes of the boundary ring beams and the rigid members and the lower ends of the adjacent inside vertical brace rods; square down string-nets are formed among the lower ends of the vertical brace rods on the horizontal symmetric axes and the vertical symmetric axes; down string-nets are connected among the adjacent nodes of the lower ends of the peripheral vertical brace rods; and four corners are provided with down string-nets. The square rigid cable dome structure is concise in structural form and excellent in stress performance, has improved bearing capacity and stability compared with beam string structures with same span and rise-span ratio, is gentle in deformation, and saves the space at the same time.