Non-adiabatic dynamical calculations are carried out for the Na ( 3 p ) + HD ( ν = 1 , j = 0 ) → NaH / NaD + D / H reaction on the diabatic potential energy surfaces of Wang et al. (Sci. Rep. 2018, 8, 17960) by using the time-dependent wave packet method. The state-to-state integral cross sections and differential cross sections of two reaction channels (NaH/NaD+D/H) are calculated for collision energy up to 0.4 eV. The cross section branching ratio indicates that the dominant reaction channel changes from NaD+H to NaH+D when the collision energy is larger than 0.227 eV. The products from two reaction channels both prefer to form in vibrationally cold but rotationally hot states, and they both tend to forward scattering.