We report a wideband wavelength-tunable ultrafast fiber laser mode-locked with a few-layer black phosphorus (BP) saturable absorber. The proposed laser not only delivers picosecond stable conventional solitons but also exhibits flexible wavelength tunability from 1529 to 1592nm. It is experimentally demonstrated that the broadband saturable absorption property of BP and birefringence filtering effects in the cavity contribute significantly to the aforementioned merits. In addition, the round-trip model is established to numerically demonstrate the spectral evolution, and numerical results are in good agreement with experimental observations. The proposed laser system is compact and wavelength-tunable, which provides an efficient solution for applications where a widely tunable ultrafast fiber laser is required.