To achieve the high PCE and simultaneously overcome the trade-off between open circuit voltage (VOC) and short-circuit current density (JSC), the reasonable design of the donor material is still a great challenge in non-fullerene polymer solar cells (PSCs). Herein, a pair of asymmetric 2D BDT-based wide band gap polymers, named PBPTBz-1Cl and PBPTBz-2Cl, respectively, were designed and synthesized through simultaneously introducing a chloro-substituted thiophene and another alkoxylphenyl groups as side chains onto the same BDT unit. As expected, the polymers PBPTBz-1Cl and PBPTBz-2Cl exhibit the deeper HOMO levels of −5.32 and −5.41 eV, respectively, compared with the HOMO value of −5.27 eV for chlorine-free substituted polymer PBPTBz-0Cl. Therefore, the PBPTBz-2Cl:IT-M based PSCs exhibited a higher Voc of 0.99 V, with an enhanced Jsc of 14.92 mA cm−2 and PCE of 7.18%. The Voc, Jsc and PCE were simultaneously enhanced from PBPTBz-0Cl:IT-M to PBPTBz-1Cl:IT-M, then to PBPTBz-2Cl:IT-M based PSCs successively. These results demonstrate that the challenge of the trade-off between Voc and Jsc could be overcome through the asymmetric strategy of the chloro-substituted thiophene and alkylphenyl groups as different side chains onto the same BDT unit. Hence, considering the low cost of starting materials and convenient introduction of chlorine atoms, the asymmetric chlorination of the side chain of BDT unit would be the great potential for achieving the high-performance PSCs.