For the first time, to the best of our knowledge, we present an all-fiber polarization-maintaining passively mode-locked picosecond laser operated at 980 nm. The laser cavity had a ring configuration with a semiconductor saturable absorber mirror as a mode-locking element. As an active medium, we used a specially designed cladding-pumped Yb-doped fiber with reduced cladding-to-core diameter ratio. The laser was self-starting and operated in the net cavity normal dispersion regime, where a spectral profile of the gain medium acted as a filter element. By intracavity spectral filtering, we achieved about 40 dB dominance of the signal wavelength at 980 nm over 1 µm emission in a highly stable picosecond pulsed regime. The corresponding simulation was performed to extend the knowledge about laser operation.