The band structure and topological properties of a 1D rhombus lattice are studied by defining three models according to the manners of intracell hopping amplitudes. Results show that in the presence of uniform intracell hopping amplitudes, degenerate topological edge states appear at the ends of the lattice. When the intracell hopping amplitudes change, the edge states change in different ways, but they are robust to a small amount of disorder. The inversion symmetry breaking modifies the degeneracy of the edge states and makes the edge states localized at one end of the lattice. Next, when local magnetic flux is introduced, the band structures of the three models are further modulated. New gaps can be opened and edge states can be induced with their different topological properties. This rhombus lattice can be a promising candidate for studying the edge states and their dependence on structural parameters and magnetic flux in 1D systems.