In order to promote the application of soft sets theory, the lattice structures of generalized intuitionistic fuzzy soft sets were studied. Firstly, the concept of generalized intuitionistic fuzzy soft sets was introduced, and some operations and some of their algebraic properties of generalized intuitionistic fuzzy soft sets were given. Then, the lattice structures of generalized intuitionistic fuzzy soft sets were discussed with four intersections and union operations. Finally, two lattice structures of generalized intuitionistic fuzzy soft sets were obtained, and it is proved that the two lattices are bounded distributive lattices.