The invention discloses a straining beam cable rod dome structure and a construction method of the straining beam cable rod dome structure. The straining beam cable rod dome structure comprises radial straining beams, circumferential straining beams, stay cables, pressing rods, annular cables, outer pressing rings and staining beam hinges, wherein different shapes and different sizes of triangular units are formed by the radial straining beams and the circumferential straining beams; the triangular units are connected to each other and share one edge to form a straining beam grid; connecting positions of the triangular units stretch downwards to form the pressing rods; each stay cable is connected with the lower ends of the pressing rods arranged at the inner sides of every two adjacent rings and the upper end of the pressing rod arranged at the outer side nearest to the stay cable, or is connected with the lower end of the pressing rod arranged at the outmost ring and the outer pressing rings; the annular cables are connected with the lower ends of the pressing rods in the same ring; the straining beam hinges are arranged at the end parts or the middle parts of the radial straining beams and the circumferential straining beams in the straining beam grid; the straining beam grid, the outer pressing rings, the pressing rods and the stay cables are mutually hinged. The invention also provides the construction method for low-altitude assembly and high-altitude tension forming. The invention provides a space tension structure for paving rigid roof materials, and construction is carried out by adopting an integrated pulling and lifting mechanism expansion method.