  In this letter, 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 will accrete the material of the DS and then drive magnetic blobs. FRBs
would be produced by the shock process between the magnetic blobs and the
stellar wind of the DS through the synchrotron maser mechanism. We show that
this model 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 as appeared in FRBs 180916.J0158+65 and 121102. The radio nebula
excited by the long-term injection of magnetic blobs into the surrounding
environment also can account for the persistent radio source associated with
FRB 121102. In addiction, we discuss in detail the possible multi-wavelength
counterparts of FRB 180916.J0158+65 in the context of this model.
Multi-wavelength observations in the future will verify or falsify this model.
