Growing efforts have been devoted to developing electron-acceptor polymers as alternatives to fullerene derivatives and realizing high-performance all-polymer solar cells (all-PSCs). Until recently, the majority of acceptor polymers used in all-PSCs are constructed with linear conjugated backbones. Star-shaped conjugated polymers, featuring three or more conjugated arms radiating like spokes from a central axle, are exceptional and providing a fascinating area of study. In this concept, the shapes of polymers can be extended to second and third (2D and 3D) dimensions and the degree of intermolecular interaction can be substantially modulated. This property is suggested to prevent the aggregation of some conventional acceptor polymers and optimize the blend morphology in all-PSCs. However, there is a dearth of systematic studies in this area. To this end, we synthesize six star-shaped acceptor polymers, in which three or four conjugated arms based on naphthalene diimide (NDI) and bithiophene share a specific core unit. The different shapes and conjugation length generated by core units modulate the molecular weights and photophysical properties of the star-shaped polymers, and the miscibility with the donor polymer in all-polymeric blends. Three of the six all-PSCs attain good power conversion efficiencies (PCEs) over 6.0% and the best PCE is 6.5%. This work discloses the synergetic effects generated by the star-shaped acceptor polymers on the performance of the all-PSCs, and also highlights an promising avenue for developing high-performing acceptor polymers by using a star-shape strategy.