Abstract: Fast Radio Bursts (FRBs) are transient and bright radio pulses from cosmological origins, which have two types: repeating FRBs and non-repeating FRBs. Based on the eccentric binary model for the origin of the periodic FRBs, we consider the effects of gravitational-wave (GW) radiation on the periodic activity of repeating FRBs. The compact binary system composed of a neutron star (NS) with a strong bipolar magnetic field and a magnetic white dwarf (WD) may be able to explain the repeated behavior of repeating FRBs. When WD fills its Roche lobe, mass transfer will occur through the inner Lagrange point to the surface of the NS. After an explosion, the WD may be kicked away owing to the conservation of angular momentum, and refills its Roche lobe at the next periastron, due to the decrease of orbital separation through GW radiation to realize another. In this scenario, the period of the repeating FRBs should be equivalent to the orbital period P_orb. Thus, the relation between P_orb and the time interval of two adjacent mass-transfer processes Δt is a key factor that may determine whether the periodic activity can show up. Obviously, Δt≈P_orb or Δt ＜ P_orb is a necessary condition for the periodic activity to appear. On the contrary, for Δt >> P_orb, the periodicity will be hard to discover. The results show that the periodic activity is more likely to show up for relatively long periods, which may be the reason that only two sources having been claimed to have periodic activity, both correspond to relatively long periods.