  We introduce the $J$-equation on holomorphic vector bundles over compact
K\"ahler manifolds and investigate some fundamental properties as well as
examples of solutions. In particular, we provide an algebraic condition called
(asymptotic) $J$-stability in terms of subbundles on compact K\"ahler surfaces,
and a numerical criterion on vortex bundles via dimensional reduction. Also, we
discuss an application for the vector bundle version of the deformed
Hermitian-Yang-Mills equation in the small volume regime.
