  We investigate the scalar mode quadrupole radiation of gravitational waves in
$F(R)$ modified gravity. In $F(R)$ gravity a massive scalar mode appears in the
gravitational waves.
  We find explicit expressions for the quadrupole radiation and the energy
current of the scalar mode in general $F(R)$ gravity models.
  We consider a binary star and a bouncing star as astronomical sources of the
gravitational waves and calculate the quadrupole radiation of the scalar and
tensor modes.
  The scalar mode radiates under spherically symmetric conditions, but the
tensor modes do not.
  The scalar mode mass is estimated for some typical energy scales. We show a
possibility to detect the scalar mode in the future gravitational waves
observation.
