  We present QCD prediction of double-spin asymmetries ($A_{TT}$) in
transversely polarized Drell-Yan process at small transverse momentum $Q_T$ of
dimuon. Resummation of large logarithmic corrections, relevant in small $Q_T$
region, is performed up to next-to-leading logarithmic (NLL) accuracy. $A_{TT}$
at RHIC, J-PARC and GSI are studied numerically in the corresponding kinematic
regions.We show that the large $A_{TT}$ is obtained for small $Q_T$ and
moderate energies.
