We report 'broadband light-sensing' all-polymer phototransistors with the nanostructured bulk heterojunction (BHJ) layers of visible (VIS) light-sensing electron-donating (p-type) polymer and near infrared (NIR) light-sensing electron-accepting (n-type) polymer. Poly[{2,5-bis-(2-ethylhexyl)-3,6-bis-(thien-2-yl)-pyrrolo[3,4-c]pyrrole-1,4-diyl}-co-{2,2'-(2,1,3-benzothiadiazole)]-5,5'-diyl}] (PEHTPPD-BT), which is synthesized via Suzuki coupling and employed as the n-type polymer, shows strong optical absorption in the NIR region (up to 1100 nm) in the presence of weak absorption in the VIS range (400~600 nm). To strengthen the VIS absorption, poly(3-hexylthiophene) (P3HT) is introduced as the p-type polymer. All-polymer phototransistors with the BHJ (P3HT:PEHTPPD-BT) layers, featuring a peculiar nano-domain morphology, exhibit typical p-type transistor characteristics and efficiently detect broadband (VIS~NIR) lights. The maximum corrected responsivity (without contribution of dark current) reaches up to 85~88% (VIS) and 26~40% (NIR) of theoretical responsivity. The charge separation process between P3HT and PEHTPPD-BT components in the highest occupied molecular orbital is proposed as a major working mechanism for the effective NIR sensing.