A new approach to design and realize a broadband multilayer anti-reflection (AR) coating is proposed in this study. The binominal multi-section transformer is employed to efficiently determine the thickness and the refractive index of each matching layer, while those layers can be further realized by doping different fraction of silicon nano powders (for relatively-high-index layers) or air pores (for relatively-low-index layers) into the low-loss HDPE polymer. Based on this scheme, we design a ten-layer AR coating for widely used silicon wafer. The designed AR coatings are double-side integrated with a 375-μm-thick silicon wafer, which is able to enhance the overall THz transmission to higher than 95.00% from 0.250 THz to 0.919 THz (114.46% bandwidth) for either TE-polarized or TM-polarized THz beam incident from arbitrary angle below 50º.