A passively mode-locked soliton laser is constructed employing semiconductor saturable absorber mirror (SESAM) as mode-locking regime. This laser only has single all-solid Yb-doped photonic bandgap fiber (AS-Yb-PBGF). At 1 μm wavelength region, the fiber has anomalous group velocity dispersion (GVD), thus it provides the laser gain and anomalous dispersion simultaneously. In the cavity, the balanced effect between the nonlinear effect and the anomalous GVD offered by the AS-Yb-PBGF can lead to soliton operation. By means of the split-step Fourier method, the dynamics of single-soliton operation in the laser is numerically simulated. At different initial signals the same stable soliton operation is finally obtained. The single-soliton operation with the pulse duration of 125 fs, the pulse energy up to 135 pJ has been shown, and the time-bandwidth product is 0.33 nearly the transform-limited pulse. The pulse repetition rate is up to 500 MHz. At the same time, the dynamics process of the pulse in the cavity is systemically studied.