Due to their advantages of low cost, flexibility and light weight, organic solar cells (OSCs) are considered to be a promising photovoltaic technology for practical applications and have received great attentions. The active layers of OSCs are the blends of conjugated small molecule/polymer electron donors and electron acceptors. Before 2013, the most-widely used electron acceptors are fullerene derivatives. Nevertheless, the weak absorption in the visible region, limited electronic tunability, and poor morphological stability hinder their further application in OSCs. Non-fullerene electron acceptors with good light harvesting ability and tunable energy levels have developed rapidly in past few years. Based on the types of electron donor and acceptor materials, non-fullerene OSCs may be classified into four types, including polymer donor/polymer acceptor blend (PD/PA), polymer donor/small molecule acceptor blend (PD/MA), small molecule donor/polymer acceptor blend (MD/PA), and small molecule donor/small molecule acceptor blend (MD/MA). Among various kinds of OSCs, MD/PA-type OSCs possess the excellent morphology stability under thermal stress, which is worthy of further study. Although the advantages of MD/PA-type OSCs, there are still large challenges in their development. The power conversion efficiencies (PCEs) of MD/PA-type OSCs are still much lower than that of other type OSCs, due to the limited material combination of small molecule donors and polymer acceptors and undesirable phase separation morphology of the active layers. In this review, we summarize the research progress of OSCs based on small molecule donors and polymer acceptors, and introduce the active layer material systems from three type polymer acceptors, i.e. the imide group, cyano group and boron-nitrogen coordination bond (B←N) unit based polymer acceptors. Benefiting from the development of both donor and acceptor materials as well as the manipulation of phase-separation morphology in active layers, the good match between small molecule donors and polymer acceptors is achieved. This not only boosts the large improvement in PCE from 0.29% to 9.51%, but also contributes to a high-temperature tolerant photovoltaic device. Finally, we also present an outlook of the future development of high-performance MD/PA-type OSCs.