Picosecond-scale, 1064 nm central wavelength, 0.4 nm 3 dB spectrum width, 17.3 MHz steady continuous wave (CW) passive mode-locked fiber laser is realized using semiconductor saturable absorber mirror (SESAM), highly-doped Yb fiber and fiber Bragg grating (FBG). In the process of increasing pump power, the pump power threshold of mode-locking start-up is 50 mW, while in the process of decreasing pump power, the minimum pump power of steady mode-locking is 37 mW. Q-switched pulse, CW passive mode-locked pulse with Q-switch fluctuation of little amplitude, double-pulse modulation, tri-pulse modulation and more pulse modulation appearing successively as the pump power are escalated. The modulation becomes unsteady in the process of splitting. The number and peak value of split pulses present uncertainty when the pump energy is high enough. The higher pump power and stronger mode-locking, the wider the spectra are. It is demonstrated that more split pulses mean narrower autocorrelation trace and shorter pulse width. The environmental disturbance may have some effect on the multi-pulse modulation.