Polarizers have been widely used in various optical systems to reduce polarization cross talk. The polarizers based on the silicon nanowire waveguide can provide chip-scale device size and a high polarization extinction ratio. However, the working bandwidth for the on-chip silicon polarizers is always limited (<～100nm) by the strong waveguide dispersion. In this paper, an on-chip all-silicon polarizer with an extremely broad working bandwidth is proposed and demonstrated. The device is based on a 180° sharp waveguide bend, assisted with anisotropic subwavelength grating (SWG) metamaterial cladding to enhance the polarization selectivity. For TE polarization, the effective refractive index for SWG is extraordinary, so the incident TE mode can propagate through the sharp waveguide bend. For TM polarization, the effective refractive index for SWG is ordinary, so the incident TM mode will be coupled into the radiation mode regardless of the wavelength. The fabricated polarizer shows low loss (<1dB) and high polarization extinction ratio (>20dB) over a >415nm bandwidth from 1.26 to 1.675 μm, which is at least fourfold better than what has been demonstrated in all previous works. To the best of our knowledge, such a device is the first all-silicon polarizer that covers O-, E-, S-, C-, L-, and U-bands.