  Motivated by our previous work on Hodge-index type inequalities, we give a
form of mixed Hodge-Riemann bilinear relation by using the notion of
$m$-positivity, whose proof is an adaptation of the works of Timorin and
Dinh-Nguy\^{e}n. This mixed Hodge-Riemann bilinear relation holds with respect
to mixed polarizations in which some satisfy particular positivity condition,
but could be degenerate along some directions. In particular, it applies to
fibrations of compact K\"ahler manifolds.
