A ytterbium (Yb)-doped fiber laser based on semiconductor saturable absorber mirror was designed. By adjusting the net dispersion in the cavity with chirped fiber Bragg grating, the output pulse characteristics of the laser were studied when the net dispersion in the cavity was in the negative dispersion region. In the experiment, the linear cavity structure with all-polarization maintaining was adopted. When the pump power was 138 mW, the stable self-starting mode-locking was realized. The minimum pulse width of the output pulse is 4.5 ps, the maximum repetition frequency is 46.5 MHz, the central wavelength is 1 063.7 nm, and the spectral width of 3 dB is 1.44 nm. When the pump power is 220 mW and the intracavity filtering bandwidth is 4 nm, the bound solitons with pulse width of 6.24 ps and pulse interval of 46.58 ps can be observed. Finally, the 12-h stability test proves that the laser has good power stability, and can be used as a stable seed source for subsequent applications.