The N( 2 D) + HD (v = 0, j = 0) reaction has been studied by a quantum time-dependent wave packet approach with a second-order split operator on the potential energy surface of Li et al. (Li Y, Yuan J, Chen M, Ma F and Sun M J. Comput. Chem. 34 1686). The rovibrationally resolved reaction probability, vibrationally integral cross section, and differential cross section of the NH + D and ND + H channel are investigated at the state-to-state level of theory. The experimental data of the thermal rate constant of two output channels is very scare, but the sum of the two output channels is in excellent agreement with the experimental data which was reported by Umemoto et al. It may imply that the thermal rate constants of the two output channels are accurate and reliable.