We report on a SESAM mode-locked all-normal-dispersion all-polarization-maintaining (PM) ytterbium-doped picosecond fiber laser. The linear cavity oscillator utilizes a narrowband filter for pulse shaping for the first time, to the best of our knowledge. Stable mode-locked pulses with a repetition rate of 29 MHz are achieved under a maximum average output power of 35.9 mW. The linearly polarized pulses have a full width at half maximum of 4nm at a central wavelength of 1032nm, and a 20.6ps pulse duration with pulse energies of 1.2 nJ. Compared to the reported experiment scheme of the generation of the picosecond pulses, the presented all-PM-fiber linear cavity mode-locked oscillator with spectral filter as pulse modulation component provides a new method for the realization of the compact-sized low-cost high-performance picosecond pulses and has important potential applications in a seeding master-oscillator power amplification system.