An alternating copolymer (P(IDT-NDI)) containing indacenodithienothiophene (IDT) and naphthalene diimide (NDI) units was synthesized for application as an acceptor material in all-polymer solar cells (all-PSCs). The polymer possesses a low bandgap of 1.51 eV, a suitable LUMO level of -3.84 eV and a HOMO level of -5.75 eV for use as an acceptor material instead of PCBM. Three conjugated polymers including J50 and J51 with a medium bandgap (ca. 1.9 eV) and PTB7-Th with a low bandgap (1.59 eV) were selected as donor materials for the investigation of the photovoltaic performance of the nonfullerene acceptor P(IDT-NDI). The champion all-PSCs with P(IDT-NDI) as an acceptor demonstrated power conversion efficiencies of 3.63%, 4.12% and 5.33% for the polymer donors PTB7-Th, J50 and J51, respectively. The results indicate that the complementary absorption of the polymer donor with polymer acceptor is very important for high performance all-PSCs and P(IDT-NDI) is a promising polymer acceptor for all-PSCs.