  We calculate \alpha^{2}\alpha_{s}^{2} order QED contribution to J/\psi
production in pp(\bar{p})\to J/\psi+c\bar{c} color-singlet process at the
Tevatron and LHC in the framework of non-relativistic QCD. The contribution of
the interference between the \alpha^{2}\alpha_{s}^{2} QED and \alpha_{s}^{4}
QCD is also taken into account. The J/\psi production associated with a charm
quark pair could be a measurable signal at hadron collider experiment. Our
calculations show that by including the QED contribution, the p_{t}
distribution is enhanced by a factor of 1.5 (1.9) at the Tevatron (LHC) at
p_{t}=50 (100) GeV. In addition, the polarization of J/\psi turns from
unpolarized in all region to increasingly transverse when p_{t} becomes larger.
