Tremendous efforts have been devoted for designing polymer acceptors to replace fullerene derivatives for high-performance all-polymer solar cells (all-PSCs). For this purpose, based on the famous copolymer acceptor PNDIT2, a series of random terpolymers are synthesized by replacing the naphthalene diimide unit with a very small amount of phosphorescent Pt complex, (dbm)PtPyTPA, which is linked through the dibenzoylmethane (dbm) ancillary ligand to the PNDIT2 backbone. The terpolymers P(dbm)PtPyTPAx, where x represents the feed ratio (1, 2 and 5 mol%) of Pt complex, exhibit comparable optical and electrochemical properties to those of the PNDIT2 copolymer. Interestingly, by blending PNDIT2 or P(dbm)PtPyTPAx polymer acceptor with the PTB7-Th polymer donor, gradually enhanced power conversion efficiency (PCE) is achieved with an increase in the Pt complex feed ratio in both the conventional and inverted configurations of all-PSCs. The terpolymer acceptor P(dbm)PtPyTPA5 shows the highest PCE with maximum/average values of 3.97%/3.88% and 4.99%/4.91% compared to 2.58%/2.54% and 3.72%/3.66%, showing 53% and 34% increase in the conventional and inverted structures, respectively. Through a combination of photoelectric measurements, it is found that the improvement in PCE is mainly due to more efficient exciton separation, less charge recombination and higher hole and electron mobilities with enhanced short current density (J_sc) and fill factor (FF). An increase in the maximum PCE value from 3.79% for PNDIT2 to 6.18% for the Pt-containing terpolymer is also observed in all-PSCs based on another polymer donor, PBDB-T. The heavy-metal-containing random terpolymer acceptors in this study afford a facile approach to improve the photovoltaic performances of all-PSCs based on current high-efficiency copolymer acceptors.