The dynamics of the Cl + HD reaction has been studied by means of quasi-classical trajectory calculations on BW2 potential energy surface. The integral cross-sections versus collision energy and the DCl/HCl product branching ratios calculated quasi-classically on BW2 potential energy surface predict a clear preference to the production of DCl over HCl, The computed results also show that the integral cross-sections and the DCl/HCl product branching ratios strongly depend on the initial rotational quantum numbers j and the vibrational quantum numbers v, The calculated results are in reasonable agreement with experimental data, and some other theoretical results as well.