Recent advances in non-fullerene acceptors (NFAs), typically Y6, have driven power conversion efficiency (PCE) of single-junction organic solar cells (OSCs) over 16%. Meanwhile, it becomes essential to know how to adopt simple strategies to further improve device performance. In this work, a new A-DA D-A acceptor derivative, Y19-N3 employing 3-ethylheptyl branched at the 3rd-position instead of 2-ethylhexyl on the pyrroles of Y19 is reported. The selection of an appropriate solvent in casting device is implemented to maximize the photovoltaic performance. PBDB-T:Y19-N3-based OSCs treated with a ternary solvent of CF/CB (1:3, v/v) and 0.8% DIO exhibit the optimal PCE of 13.77% here, with the significantly improved Voc (0.78 V) and FF (0.72) as well as the high Jsc (24.46 mA/cm2). Further characterizations indicate that this ternary solvent-treated PBDB-T/Y19-N3 film exhibits the more appropriate morphological features with the highly efficient charge generation and collection as well as the more balanced electron and hole mobilities. This work combines molecular design and device engineering to improve the photovoltaic properties, which is important to the development of OSCs.