We　report　on　an　all-fiber　passively　mode-locked　ytterbium-doped　(Yb-doped)　fiber　laser　with　single　polymer　composite　saturable　absorber　(SA)　based　on　the　single　wall　carbon　nanotubes　(SWCNTs)　with　diameters　of　0.8　nm.　The　SWCNTs　are　mixed　with　sodium　carboxymethylcellulose　(NaCMC)　to　form　SWCNTs　SA　film.　The　non-saturable　absorption　coefficient,　modulation　depth　and　saturable　intensity　of　the　SWCNTs　SA　are　measured　to　be　29%,　12%　and　0.12　MW/cm(2),　respectively.　By　using　the　SWCNTs　as　SA,　a　passively　mode-locked　Yb-doped　fiber　laser　has　been　achieved　at　979　nm　with　pulse　duration　of　228　ps　and　repetition　rate　of　15.47　MHz.　To　our　knowledge,　this　is　the　first　time　ever　reported　in　an　all-fiber　Yb-doped　mode-locked　fiber　laser　using　SWCNTs　as　SA　at　980　nm,　which　overcome　the　difficulties　of　low　gain　and　serious　re-absorption　effects　in　the　quasi-three-level　system.　In　order　to　verify　the　saturation　absorption　performance　of　the　SWCNTs,　mode-locking　experiment　in　quasi-four-level　system　is　also　carried　out　around　1030　nm　and　the　stable　and　uniform　mode-locked　pulses　are　obtained.　A　mode-locked　fiber　laser　at　1032　nm　is　realized　with　a　pulse　width　of　485　ps　and　repetition　rate　of　8.78　MHz.　It　is　sufficiently　manifested　that　SWCNTs　with　diameters　of　0.8　nm　have　excellent　saturable　absorption　performance　as　optical　mode-locking　elements　in　ultrafast　photonic　applications.