Donor-acceptor-acceptor (D-A-A) type 1,8-naphthalimide based small molecules SM1 and SM2 functionalized with tetracyanobutadiene (TCBD) and dicyanoquino-dimethane (DCNQ) modules, showing strong absorption in the visible and near-infrared (NIR) region are reported. TCBD and DCNQ linked SM1 and SM2 exhibit multi-redox waves. The electrochemical and optical HOMO-LUMO gaps show similar trends. These SMs exhibit a broad absorption profile which is complementary to the D-A copolymer P donor and also possess an appropriate lowest unoccupied molecular orbital (LUMO) to serve as an acceptor with P with a LUMO level of -3.33 eV. The organic solar cells based on P:SM1 and P:SM2 exhibit a PCE of 4.94% and 6.11%, respectively. The higher value of the PCE for the SM2 based organic solar cells has been attributed to the broader absorption profile, more balanced charge transport and lower photon energy loss. The values of Voc of the organic solar cells for the SM1 acceptor (1.06 V and 1.02 V without and with solvent additive) are the highest values reported for devices based on non-fullerene acceptors to the best of our knowledge. The energy loss (Eloss) of 0.56 eV and 0.48 eV for SM1 and SM2 based devices, respectively is one of the smallest reported for BHJ organic solar cells.