An electron acceptor in a bulk heterojunction (BHJ) is one of the significant factors for the performance of organic solar cells (OSCs). Acceptors are required to possess an appropriate energy level to be well fitted with donors and a complementary absorption profile in the near-infrared (NIR) region of solar spectra. Herein, two novel star-shaped electron acceptors TBT-1 and TBT-2 denoted as 3a and 3b, respectively, based on a planar truxene core conjugated with three 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) units were designed. Both 3a and 3b show strong absorption in both visible and NIR regions in solution and in films. Due to the strong electron-donating capability of the dimethylamino group and a good π-conjugative effect, 3a displays a slightly higher highest occupied molecular orbital (HOMO) level (−5.40 eV) and a deeper lowest unoccupied molecular orbital (LUMO) level (−3.96 eV) compared to 3b (HOMO = −5.52 eV and LUMO = −3.94 eV), resulting in red-shifted absorption, showing a narrower optical band gap of 1.44 eV than that of 3b (1.58 eV). When blended with a donor polymer P, the OSCs based on P:3a and P:3b exhibit a superior short-circuit current density (J sc ), high electron mobility, and open-circuit voltage (V oc ). OSCs based on optimized P:3a and P:3b exhibit the best power conversion efficiency (PCE) values of 13.41 and 11.75%, respectively. To the best of our knowledge, this is among the best values for OSCs with a non-fullerene small-molecule acceptor (NFSMA) based on BODIPY derivatives. These outcomes suggest that integrating extended conjugation into a star-shaped building block encourages designing high-performance NFSMAs for application in OSCs.