Since many or most galaxies have central massive black holes (BHs), mergers
of galaxies can form massive binary black holes (BBHs). It is possible tha
t some BBHs exist in active galactic nuclei (AGNs). We argue that each BH m
ay be surrounded by an accretion disc with a different inclination angle to
the line of sight (due to different BH spin directions and the Bardeen-Pet
terson effect). The observed Fe K alpha line profile from a BBH system is a
combination of the lines from the inner regions of the two discs, which is
significantly affected by the inclination angles of the two discs. The Fe
K alpha line profile associated with BBHs may have an unusual shape with do
uble or more peaks as well as short-term variability (e.g.similar to 10(4)
s), which can be distinguished from the Fe K alpha line properties of some
other possible models. The precession of the two discs could introduce two
un-related quasi-periodic signals in the X-ray continuum emission, which wo
uld be useful to constrain both of the BH masses. We suggest that with the
improvement of resolution in X-ray astronomy, Fe K alpha line profiles be a
potential tool to probe the existence of massive BBHs in AGNs. The Fe K al
pha line profile associated with BBHs may also provide a tool to investigat
e the dynamics in strong gravitation field (e.g. providing evidence of the
Bardeen-Petterson effect).