The double longitudinal-spin asymmetry, ALLβ, of the J/Ο production
in polarized proton-proton collisions is presented in this paper at QCD
next-to-leading order. It is found that the obtained values of ALLβ are in
general consistent with the PHENIX measurements. Various sets of the
long-distance matrix elements (LDMEs) are employed in our calculation to study
the possible theoretical uncertainties. It is found that, for p_t<5\gev, all
these LDMEs lead to almost the same results, which are within the tolerance of
the experimental data uncertainties