The external force can make a graphene sheet tighten and change its electronic structure. By using the tight-binding method, the energy bands of graphene sheets with zigzag shaped edges and armchair shaped edges drawn by the tensile force are investigated based on considering the nearest-neighbor interaction, and the analytic relations between the energy gaps besides the energy bands of π-electrons for two types of graphene sheets and the tensile force are obtained . Through numerical calculation, we found that the energy gaps broaden as the tensile force increases besides that the tensile force can make graphene open an energy gap,and moreover, the energy gap of graphene with zigzag edges broadens more easily.