The introduction of quinoidal character to pi-conjugated polymers is one of the effective approaches to reducing the bandgap. Here we synthesized new pi-conjugated polymers (PBTD4T and PBDTD4T) incorporating thienoquinoids 2,2'-bithiophene-5,5'-dione (BTD) and benzo[1,2-b:4,5-b']-dithiophene-2,6-dione (BDTD) as strong electron-deficient (acceptor) units. PBTD4T showed a deep LUMO energy level of -3.77 eV and a small bandgap of 1.28 eV, which are similar to those of the analog using thieno[3,2-b]thiophene-2,5-dione (TTD) (PTTD4T). PBDTD4T had a much deeper LUMO energy level of -4.04 eV and a significantly smaller bandgap of 0.88 eV compared to those of the other two polymers. Interestingly, PBDTD4T showed high transparency in the visible region. The very small bandgap of PBDTD4T can be rationalized by the enhanced contribution of the resonance backbone structure in which the p-benzoquinodimethane skeleton in the BDTD unit plays a crucial role. PBTD4T and PBDTD4T exhibited ambipolar charge transport with more balanced mobilities between the hole and the electron than PTTD4T. We believe that the very small bandgap, i.e., the high near-infrared activity, as well as the well-balanced ambipolar property of the pi-conjugated polymers based on these units would be of particular interest in the fabrication of next-generation organic devices.