Lately, non-fullerene acceptors (NFAs) have received increasing attention for use in polymer-based bulk-heterojunction (BHJ) organic solar cells (OSCs), as improved photovoltaic performance compared to classical polymer–fullerene blends could be demonstrated. In this study, polymer solar cells based on a statistically substituted anthracene-containing poly(p-phenylene ethynylene)-alt-poly(p-phenylene vinylene)s (PPE–PPVs) copolymer (AnE-PVstat) as donor in combination with a number of different electron accepting materials were investigated. Strong photoluminescence quenching of the polymer donor indicates intimate intermixing of both materials. However, the photovoltaic performances were found to be poor compared to blends that use fullerene as acceptor. Time-delayed collection field (TDCF) measurements demonstrate: charge generation is field-independent, but bimolecular recombination processes limit the fill factor and thus the efficiency of devices.