The low-temperature plasticity of aluminum nitride (AlN) is determined by the interaction between edge and screw dislocations. However, the motion of screw dislocations and their glide mechanisms have not been evaluated. In this study, the motion of a ⟨0001⟩{11̅ 00} screw dislocation in a single crystal of AlN is explored by molecular dynamics simulations using LAMMPS software with the Stillinger−Weber (SW) potential. Four modes of thermally activated motion are observed under different conditions of temperature and stress: double kinks, Shockley partials, self-pinning, and debris and dislocation loops. The mobilities of a ⟨0001⟩{11̅ 00} screw dislocation and a 1/3⟨112̅ 0⟩{11̅ 00} edge dislocation are compared under various conditions. Our results show that the mobilities of the ⟨0001⟩{11̅ 00} screw and 1/3⟨112̅ 0⟩{11̅ 00} edge dislocations are quite low at T < 600 K. The ⟨0001⟩{11̅ 00} screw dislocation moves faster at 900 < T < 1500 K and seems less dependent on the temperature than does the 1/3⟨112̅ 0⟩{11̅ 00} edge dislocation at 1200 < T < 2200 K. However, the opposite phenomenon is observed at higher temperatures. The mobility of the ⟨0001⟩{11̅ 00} screw dislocation is slightly lower than that of the 1/3⟨112̅ 0⟩{11̅ 00} edge dislocation at T > 1800 K, although the mobility difference can reach several orders of magnitude at 900 < T < 1200 K due to different Peierls barriers.