The lasing characteristics of a 365 kHz low repetition rate Yb-doped fiber laser operated in an all-normal dispersion cavity and mode-locked by the nonlinear polarization rotation mechanism are investigated in detail. As the pump power increases, the laser exhibits two transition routes when evolved from the continuous-wave (CW) state to the mode-locked (ML) state. In one evolution route the Q-switched mode-locked (QML) state is sandwiched between the CW and ML states, whereas in the other more interesting evolution route the hysteresis transition between the CW and ML states is found for the first time. Under the mode-locking operation, the laser generates sub-nanosecond pulses with linear dependence of pulsewidth on bandwidth under different pump powers, indicating the presence of giant linear chirps on the laser output pulses.