  We consider a contribution to J/psi hadroproduction in which the meson
production is mediated by three-gluon partonic state, with two gluons coming
from the target and one gluon from the projectile. This mechanism involves
double gluon density and thus it enters at a non-leading twist, but it is
enhanced at large energies due to large double gluon density at small x. The
three-gluon contribution to J/psi hadroproduction is calculated within
perturbative QCD in the k_T factorization framework, and it is found to provide
a significant correction to the standard leading twist cross-section at the
energies of the Tevatron or the LHC. The results are given as differential
p_T-dependent cross-sections for J/psi polarization components.
