The transverse momentum (p(t)) distributions of production and polarization for J/psi measured by CDF Collaboration are still challenging our understanding of the heavy quarkonium production mechanism even with recent significant theoretical progresses on the next-to-leading-order (NLO) QCD calculation. We investigate an interesting mechanism for J/psi production at hadron collider, pp((p) over bar) -> gamma* (J/psi) + X with J/psi from a virtual photon gamma* fragmentation. Our calculations show that the J/psi p(t) distribution in the photon fragmentation process up to NLO in alpha(s) will be larger than that of the conventional J/psi production from the color-singlet mechanism at NLO when p(t) > 26 (35) GeV at the Tevatron (LHC) and reach about 6 (10) times of the conventional one when p(t) = 50 (100) GeV at the Tevatron (LHC), in spite of a suppression factor (alpha/alpha(s))(2) that is associated with the QED and QCD coupling constants. In addition, it also has large impact on the p(t) distribution of J/psi polarization in large p(t) region. Therefore, it is an important mechanism for J/psi production at large p(t) region especially for the LHC. (c) 2012 Elsevier B.V. All rights reserved.