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We reported numerically and experimentally the dissipative soliton operation from a dispersion-managed passively mode-locked erbium fiber laser based on carbon nanotubes (CNTs). Outside compressing the dissipative soliton pulses with spectral width of 35 nm, pulses with 95 fs duration have been obtained. Harmonic mode-locking of the dissipative solitons has also been observed. It suggests that the formation of harmonic mode-locking in mode-locked fiber lasers is independent of the concrete features of the solitons. Additionally, we numerically and experimentally showed that the net dispersion value play a crucial role on the operation regimes of the dispersion-managed fiber laser and the characteristics of the output pulses.