With the quasi-classical trajectory method the stereodynamics of the O+DCl→OD+Cl reaction on the ground potential energy surface is investigated. The characteristic of calculated integral cross-section is consistent with that of the non-energy barrier reaction path on the potential energy surface, which implies that the title reaction is a typical exothermic reaction. The obtained differential reaction cross-section shows that the products tend to both forward and backward scattering, and the forward scattering is stronger than the backward one. So we can infer that the reaction follows the indirect reaction mechanism that has been verified by the randomly abstractive reaction trajectories. The distribution curves of P(θr) and 2(J'· K)> reflect that the degree of rotational alignment of the product OD first increases and then decreases with collision energy increasing. The product rotational angular momentum vector J' is aligned along the y-axis direction but is oriented along the positive direction of y-axis at higher collision energy. With the increase of the collision energy the rotation mechanism of the product molecules transits from the “in-plane” mechanism to the “out-of-plane” mechanism.