To achieve efficient organic solar cells, the design of suitable donor-acceptor couples is crucially important. State-of-the-art donor polymers used in fullerene cells may not perform well when they are combined with non-fullerene acceptors, thus new donor polymers need to be developed. Here we report non-fullerene organic solar cells with efficiencies up to 10.9%, enabled by a novel donor polymer that exhibits strong temperature-dependent aggregation but with intentionally reduced polymer crystallinity due to the introduction of a less symmetric monomer unit. Our comparative study shows that an analogue polymer with a C2 symmetric monomer unit yields highly crystalline polymer films but less efficient non-fullerene cells. Based on a monomer with a mirror symmetry, our best donor polymer exhibits reduced crystallinity, yet such a polymer matches better with small molecular acceptors. This study provides important insights to the design of donor polymers for non-fullerene organic solar cells.