  We investigate the $Q^{2}$-evolution of the chiral-odd spin-dependent parton
distribution $h_{L}(x, Q^{2})$ relevant for the polarized Drell-Yan processes.
The results are obtained in the leading logarithmic order in the framework of
the renormalization group and the standard QCD perturbation theory. We
calculate the anomalous dimension matrix for the twist-3 operators for $h_{L}$
in the one-loop order. The operator mixing among the relevant twist-3 operators
including the operators proportional to the QCD equations of motion is treated
properly in a consistent scheme. Implications for future experiments are also
discussed.
