We experimentally demonstrated a Q-switched mode-locked (QML) and a continuous-wave mode-locked (CWML) ytterbium-doped fiber lasers with topological insulator: as saturable absorber (SA) in all normal dispersion regime. The is conventionally composited by embedding nanoplatelets into polyvinyl alcohol thin film, which provides a modulation depth of 7.6% and a saturation intensity of . Based on this SA, with different cavity length, ytterbium-doped fiber laser can be operated at QML and CWML state, respectively. In the QML operation, a Q-switched envelope has the shortest pulse width of and the tunable repetition rate from 96 to 175 kHz. The largest pulse envelope energy is 39.6 nJ, corresponding to average output power of 6.93 mW. In the CWML operation, an environmentally stable dissipative soliton laser pulse with pulse duration of is obtained. The single pulse energy is 0.83 nJ with the repetition rate of 11.38 MHz at the wavelength of 1037 nm.