We comprehensively investigated the concentration effect of dispersed single-walled carbon nanotubes (SWCNTs) in polymer films for being a saturable absorber (SA) to stabilize the mode locking performance of the Erbium-doped fiber laser (EDFL) pulse through the diagnosis of its nonlinear properties of SA. The measured modulation depth was 1 to 4.5% as the thickness increased from 18 to 265 £gm. We obtained the stable pulse of the mode-locked EDFL (MLEDFL) when the full-width half-maximum (FWHM) decreased from 3.43 to 2.02 ps as the concentrations of SWCNTs SA increased from 0.125 to 0.5 wt%. At constant concentration of 0.125 wt%, the similar pulse shortening effect of the MLEDFL was also observed when the FWHM decreased from 3.43 to 1.85 ps was the thickness of SWCNTs SA increased from 8 to 100 £gm. In EDFL system, we vary group-velocity dispersion (GVD) with different cavity length to achieve optical pulse compression. We got the shortest pulsewidth was 713 fs, and the time-bandwidth product (TBP) was 0.345. An in-depth study on the stable mode-locked pulse formation employing SWCNTs SA, it is possible to fabricate the SWCNT films for use in high performance MLEDFL and utilization of many other low-cost nanodevices.