We perform a complete study on the $J/\psi$ pair hadroproduction at
next-to-leading order (NLO) in the nonrelativstic-QCD (NRQCD)
framework with the pair of $c\bar{c}$ either in ${}^{3}S_1^{[1]}$ or
${}^{1}S_0^{[8]}$ fock state. It is found that the ${}^{1}S_0^{[8]}$
channel contribution at NLO is essential. Our results indicate that
for the CMS, the NRQCD predictions can not describe the experimental
data at all, and the total cross section predicted by NRQCD is
smaller than the experimental data by an order of magnitude. So new
mechanisms are needed to understand the CMS data for $J/\psi$ pair
production. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.