Bulk heterojunction organic solar cells based on conjugated polymers and soluble fullerene derivatives have been intensively studied due to their simple device structure, easy thin-film casting process, low fabrication cost, and high power conversion efficiency. To further enhance the efficiency, it is of paramount importance to develop new p-type polymeric semiconductors with high charge mobility and narrow energy band gaps. In this paper, we report on an innovative way to synthesize low band-gap conjugated polymers with high crystallinity and reasonable solubility for wet process by using electron-acceptor cored regioregular oligothiophenes as building blocks. These novel building blocks can copolymerize with coplanar fused aromatic compounds, such as indolo[3,2-b]carbazole, to form crystalline polymers with enhanced interchain interaction. Two alternating copolymers P(InCzThnBTD) (n = 2-3) synthesized in this work show much narrower optical band gaps than widely used regioregular P3HT. In addition, the first ionization energy of both synthesized polymers remains high at ~5.17 eV, which is important to achieve large open-circuit voltage (Voc) and improve air stability. Remarkably, the bulk heterojunction photovoltaic (PV) cells fabricated from P(InCzTh2BTD) and PC61BM exhibited a promising PV performance with a PCE = 3.6 %, Voc = 0.69 V, Jsc = 9.17 mA/cm2, and FF = 0.57.