Conventional soliton (CS) and noise-like pulse (NLP) are two different kinds of pulse regimes in ultrafast fiber lasers, which have many intense applications. In this article, we experimentally demonstrate that the pulse regime of an Er-doped fiber laser could be converted between conventional soliton and noise-like pulse by using fast response saturable absorbers (SA) made from different layers of single-wall carbon nanotubes (CNT). For the monolayer (ML) single-wall CNT-SA, CS with pulse duration of 439 fs at 1560 nm is achieved while for the bilayer (BL) single-wall CNT, NLP at 1560 nm with a 1.75 ps spike and a 98 ps pedestal is obtained. The transition mechanism from CS to NLP is investigated by analyzing the optical characteristics of ML and BL single-wall CNT. The further theoretical simulation illustrates that CNT-SA enables the switching between CS and NLP in anomalous dispersion regime in Er-doped fiber lasers.