  We study prompt J/psi-meson hadroproduction invoking the hypothesis of gluon
Reggeization in t-channel exchanges at high energy and the factorization
formalism of nonrelativistic quantum chromodynamics at the leading order in the
strong-coupling constant alpha_s and the relative velocity of quarks v. The
transverse-momentum distribution of direct and prompt J/psi-meson production
measured at the Fermilab Tevatron fitted to obtain the nonperturbative
long-distance matrix elements, which are used to predict prompt J/psi
production spectra at the CERN LHC. At the numerical calculation, we adopt the
Kimber-Martin-Ryskin and Blumlein prescriptions to derive unintegrated gluon
distribution function of the proton from their collinear counterpart, for which
we use the Martin-Roberts-Stirling-Thorne set. Without adjusting any free
parameters, we find good agreement with measurements by the ATLAS, CMS and LHCb
Collaborations at the LHC at the hadronic c.m. energy sqrt S=7 TeV.
