The invention discloses a support lattice shell of a concrete spherical shell structure and a construction method. The support lattice shell of the concrete spherical shell structure comprises radial steel tubes, annular steel tubes, annular components of expansion bolts, annular components of built-in fittings, the expansion bolts, the built-in fittings, a concrete wall body, frameworks, spherical shell concrete beams, concrete shells, a support lattice shell, fragment lattice shells, through holes and fixing plates of the built-in fittings. In the construction process of the construction method, firstly the radical steel tubes and the annular steel tubes are mounted one segment by another, and are fixed to a concrete wall body structure through the annular components, and finally the frameworks are laid to form a support lattice shell of the spherical shell structure. By adoption of the construction method, the structure accuracy can be guaranteed, supporting and arranging difficulties of the frameworks can be reduced, and the construction efficiency and the construction quality can be improved. In addition, the support lattice shell of the spherical shell structure is a steel structure, can be recycled, not only can decrease wood consumption, but also is environmentally friendly; and the problems that the molding accuracy of the concrete wall body structure is low and the support system of the concrete wall body structure is difficult are solved, and the problem of framework construction of the concrete wall body structure is solved.