Developing non-fullerene acceptors (NFAs) by modifying the backbone, side chains and end groups is the most important strategy to improve the power conversion efficiency of organic solar cells (OSCs). Among numerous developed NFAs, Y6 and its derivatives are famous NFAs in the OSC field due to their good performance. Herein, in order to understand the mechanism of tuning the photovoltaic performance by modifying the Y6's center backbone, π-spacer and side-chains, we selected the PM6:Y6 OSC as a reference and systematically studied PM6:AQx-2, PM6:Y6-T, PM6:Y6-2T, PM6:Y6-O, PM6:Y6-1O and PM6:Y6-2O OSC systems based on extensive quantum chemistry calculations. The results indicate that introducing quinoxaline to substitute thiadiazole in the backbone induces a blue-shift of absorption spectra, reduces the charge transfer (CT) distance (Δd) and average electrostatic potential (ESP), and increases the singlet-triplet energy gap (ΔEST), CT excitation energy and the number of CT states in low-lying excitations. Inserting thienyl and dithiophenyl as π spacers generates a red-shift of absorption spectra, enlarges Δd and average ESP, and reduces ΔEST and the number of CT states. Introducing furo[3,2-b]furan for substituting one thieno[3,2-b]thiophene unit in the Y6's backbone causes a red-shift of absorption spectra and increases ΔEST, Δd and average ESP as well as CT excitation energy. Introducing alkoxyl as a side chain results in a blue-shift of absorption spectra, and increases ΔEST, Δd, average ESP, CT excitation energy and the number of CT states. The rate constants calculated using Marcus theory suggest that all the molecular modifications of Y6 reduce the exciton dissociation and charge recombination rates at the heterojunction interface, while introducing furo[3,2-b]furan and alkoxyl enlarges CT rates.