The　output　characteristics　of　the　Er-doped　mode-locked　fiber　laser　using　a　single-walled　carbon　nanotube　saturable　absorber　are　investigated　theoretically　with　a　nonlinear　Schrodinger　equation　and　a　saturable　absorption　equation　using　realistic　parameters.　Stable　self-starting　mode-locking　pulses　are　achieved　under　net　normal,　net　zero,　and　net　anomalous　cavity　group　velocity　dispersion　(GVD)　respectively.　A　spectrum　with　a　flat　top　is　obtained　from　the　net　normal　cavity　GVD　laser　while　a　spectrum　with　Kelly　side-bands　is　obtained　from　the　net　anomalous　cavity　GVD　laser.　The　characteristics　of　the　pulse　duration　changing　with　cavity　GVD　and　modulation　depth　of　the　single-walled　carbon　nanotubes　are　discussed.　The　characteristics　of　the　mode-locking　pulses　from　net　normal,　net　zero,　and　net　anomalous　cavity　GVD　mode-locked　fiber　lasers　are　compared.　These　systematical　results　are　useful　for　designing　mode-locked　fiber　lasers　with　saturable　absorbers　made　by　different　kinds　of　carbon　nano-materials.