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We propose an all-silicon design of a multi-band transverse-magnetic-pass (TM-pass) polarizer. The device is based on one-dimensional gratings that work under different regimes that depend on the polarization. With a tapered structure, it is revealed that the operation bandwidth can be extended by multiplexing the diffraction in O-band and the reflection in S-, C-, and L-bands for the transverse-electric (TE) mode. By simulation, we achieve a 343 nm device bandwidth with insertion loss (IL) < 0.4 dB and polarization extinction ratio (PER) > 20 dB. The operation wavelength range covers commonly-used optical telecommunication bands including the O-, S-, C-, and L- bands. Experimental results also show IL < 1.6 dB and PER > 20 dB from 1265 nm to 1360 nm corresponding to the O-band, and from 1500 nm to 1617 nm that corresponds to the C-band. The device is a single-etched design on the standard 220 nm silicon-on-insulator (SOI) with silicon oxide cladding. Such a simple and compatible design paves the way for developing practical multi-band silicon photonic integrated circuits.