We report the generation of widely wavelength tunable conventional solitons (CSs) and dissipative solitons (DSs) in an erbium-doped fiber laser passively mode-locked by nanotube saturable absorber. The tuning ranges of CSs and DSs are ∼15 and ∼25 nm, respectively. In anomalous dispersion regime, the output CS exhibits symmetrical spectral sidebands with transform-limited pulse duration of ∼1.1 ps. In the contrastive case of normal dispersion regime, the DS has rectangular spectrum profile and large frequency chirp, which presents pulse duration of ∼13.5 ps, and can be compressed to ∼0.4 ps external to the cavity. This fiber laser can provide two distinct types of tunable soliton sources, which is attractive for practical applications in telecommunications.