  In this paper we investigate the inclusive associated production of
{\Upsilon} + {\gamma} at the hadron collider. We calculate the color-singlet
sub-processes and all three color-octet sub-processes at the next-to-leading
order. Seven sets of long distance matrix elements(LDMEs), which are extracted
from the studies on the prompt production of {\Upsilon} at hadron colliders,
are used to give the numerical results and we find that there are three sets of
LDMEs give the unphysical results on the yield and the polarization for this
process. The yield is enhanced by several or two orders times comparing to that
of color-singlet process and the polarization changes from longitudinal to
slightly transverse or even mainly transverse in the large pt region. The
estimation results indicate that to study the process at the large hadron
collider (LHC) is difficult and it may be well investigated at the future Super
Proton-Proton Collider(SPPC).
