  We investigate the gravitational wave production induced by the primordial
magnetic fields in a parity-violating magnetogenesis model. It is shown that
the gravitational waves detectable by LISA, DECIGO or BBO and the magnetic
fields strong enough to explain the blazar observation can be simultaneously
produced. The magnetic fields and the gravitational waves have the same
chirality and their amplitudes are related, which may also be tested by future
observations.
