Abstract In this work, we propose an accreting stellar binary model for understanding the active periodic fast radio bursts (FRBs). The system consists of a stellar compact object (CO) and a donor star (DS) companion in an eccentric orbit, where the DS fills its own Roche lobe near the periastron. The CO accretes the material from the DS and then drives relativistic magnetic blobs. The interaction between the magnetic blobs and the stellar wind of the DS produces a pair of shocks. We find that both the reverse shock and the forward shock are likely to produce FRBs via the synchrotron maser mechanism. We show that this system can in principle sufficiently produce highly active FRBs with a long lifetime, and also can naturally explain the periodicity and the duty cycle of the activity that appeared in FRBs 180916 and 121102. The radio nebula excited by the long-term injection of magnetic blobs into the surrounding environment may account for the associated persistent radio source. In addiction, we discuss the possible multiwavelength counterparts of FRB 180916 in the context of this model. Finally, we encourage the search for FRBs in ultraluminous X-ray sources.