Considering that the variation of the modal characteristics for the TM mode is significantly larger than that for the TE mode when graphene is involved in a silicon-based waveguide, a silicon waveguide TE-pass polarizer with few-layer graphene embedded is proposed and demonstrated. Such a polarizer shows the performance merits including ultrahigh extinction ratio, low insertion loss for the TE mode, ultracompact footprint, and tunable bandwidth by dynamically varying the chemical potential of graphene with gate voltage. We further reveal that the operation bandwidth can be significantly enlarged by cascading multiple polarizers, each of which consists of a silicon waveguide embedded with few-layer graphene and is biased at different gate voltages. We numerically demonstrate that using a cascade of seven polarizers, it is capable of achieving 20-dB extinction ratio and ultralow insertion loss for the TE mode (<0.13 dB) with bandwidth over 120 nm at telecommunication wavelengths.