In this paper,the topological properties of two-component Fermi gas driven by spin-orbit coupling and Zeeman field in a one-dimensional sawtooth lattice were studied.The energy spectrum of system was calculated theoretically,and some quantities such as the edge state,von Neumann entropy,entanglement spectrum and excitation energy gap were computed numerically by matrix product state (MPS).The topological properties of the system were analyzed based on these results.It was found that the presence of edge states can be used to demonstrate the topology of the system at half filling.With the 1/4 (or 3/4) fill factor although the system has a single edge state,it does not possess other features of the general topological state.Therefore,such edge state cannot characterize the topological state.