Using the density-functional theory in combination with nonequilibrium Green's function technique, we studied the densities of states and transport properties of the(7，0)—(8，0)and(8，0)—(9，0)single-wall carbon-nanotube heterojunctions containing one pentagon-heptagon-pair (5/7) topological defect. The result suggests that the effect of pentagon-heptagon-pairs (5/7) topological defects on carbon nanotubes is remarkable.In addition, the heterojunctions constituted by different types of carbon nanotubes also have different characteristics.