Herein, we designed and synthesized two novel donor-acceptor1-acceptor2-acceptor1 (D-A1-A2-A1) type random conjugated terpolymers, DTP-TPD-DPP and DTP-TPD-BT, as a donor component for single-junction non-fullerene organic solar cells. The terpolymers were randomly combined from N-aryldithienopyrrole (DTP) donor unit and N-alkylthienopyrroledione (TPD) acceptor unit with electron-accepting dibrominated acceptor units including diketopyrrolopyrrole (DPP) or bithiophenebenzothiadiazole (TBT) by direct arylation polycondensation. Compared to two different acceptor units in the polymer backbone, DTP-TPD-DPP containing DPP exhibits stronger intramolecular charge transfer. Thus, the single-layer organic solar cells based on DTP-TPD-DPP:ITIC (1:1) demonstrated a power conversion efficiency (PCE) of 2.92 % and a high open-circuit voltage Voc of 1.0 V while devices using DTP-TPD-BT obtained a PCE of 2.64 % under the same condition fabrication in the ambient condition without any additives. The results showed that random conjugated terpolymer is an efficient and straightforward synthetic strategy to explore promising donor materials for high-performance single-junction organic solar cells.